In just a few months, The Simpsons has become the shining star in Fox's lineup, a regular entry in the Nielsen top 15 despite the fact that at its heart this is guerrilla TV, a wicked satire masquerading as a prime-time cartoon.

The Simpsons of Springfield are dysfunctional in the extreme, a family of unwitting victims who have no idea why life keeps knocking them around. Homer Simpson works in the local nuclear plant, a safety inspector who sleeps on the job. He's the leading candidate to replace Ronald Reagan as America's most befuddled father figure. His response to practically any crisis is to mutter unintelligibly and slap himself on the forehead. This is not your standard cartoon hero.

It takes six months to complete a half hour episode of The Simpsons. It's a twisted journey that spans two continents, costs more than a half-million dollars per show, requires lots of math, and, most of all, involves practically no one who wears a tie.

How do those scores of people do it? They're not really sure. Every week, it seems, they barely finish on time. The production marathon invariably ends in a desperate deadline sprint. Dialogue is changed at the last minute, scenes rewritten even after the animation is done. On most Saturday nights, less than 24 hours before the show goes on the air, the producers are still working, still adding sound effects, still fiddling with anything left to be fiddled with.

Ay, caramba!, as Bart Simpson would say.

''The last 10 days are really very hairy,'' explains Sam Simon, who shares executive producer credits with James L. Brooks and the show's creator, cartoonist Matt Groening. ''When I used to work on Taxi or Cheers, we'd usually have three weeks to edit a show at our leisure. But with The Simpsons, we usually don't see the completed show until the night before it airs. It's all very down to the line.''

In fact, the production process is not unlike the opening montage that begins every Simpsons episode, the frenetic scenes where we see family members Homer, Marge, Bart, Lisa, and Maggie careening toward home, a collection of accidents waiting to happen. They bolt out of doorways, and screech around corners, averting potential disaster at every turn.

It's a miracle that any of them make it alive, but every week they somehow manage to emerge from the chaos, just in time for the start of the show.

The production of a Simpsons episode starts with the executive producers and writers locked in a room — or, more precisely, a suite at the St. James' Club, a members-only hotel in Hollywood.

Simon says, ''We just shut off all the phones and come up with story ideas.''

Last year, only Groening, Brooks, and Simon concocted the basic plot lines. Now there's a staff of writers (with credentials that range from Saturday Night Live and Late Night with David Letterman to Harvard Lampoon) who sit in on the initial story meetings. All of them toss out scenarios, story lines, jokes, whatever pops into their heads.

This tag-team approach to creative writing is a new experience for Groening. After 10 years of drawing ''Life in Hell,'' the anxiety-ridden comic strip that is the spiritual and stylistic forerunner of The Simpsons, he was accustomed to working alone. But Groening, 36, was ready for a change. ''I definitely wanted to do this,'' he says. ''It meant an end to my loneliness.''

Even so, Groening says he might never have taken a shot at television if not for Brooks, the Academy Award-winning writer and director (Terms of Endearment, Broadcast News) who was also behind some of television's most celebrated comedy series, including The Mary Tyler Moore Show and Taxi. It was Brooks who first approached Groening about creating one-minute animated versions of ''Life in Hell'' to be used between segments of The Tracey Ullman Show. Rather than surrender the rights to his comic strip characters, Groening created a whole new brood, the Simpsons, who made their debut in April 1987, on the third episode of the Ullman show.

''First of all, I was just honored that (Brooks) liked my little cartoon,'' Groening says, ''but also it was his clout that allowed the show to be made without compromise.''

As story lines are being developed, Groening has three main concerns. He doesn't want the show to pull punches just because it's a cartoon, and he doesn't want jokes or plots to be ''too sitcommy.'' The Simpsons, he insists, is meant for adults. On the other hand, he doesn't want the show to be too dark. And this from a man who once titled a cartoon ''If parents love you so much, how come they do such awful stuff to you?''

''A lot of humor writers, when the boundaries are loosened up, don't get funnier; they get meaner,'' Groening says. ''That's something I really didn't want to happen with The Simpsons. And it hasn't.''

After the hotel session, the surviving story lines are blocked out on index cards, and each episode is assigned to a writer, who comes up with a working script. Then there is a series of rewrite meetings, with Groening, Simon, and the rest of the staff heavily involved.

''Everybody throws things in,'' Groening says, ''including a lot of people who don't get credit. That happens all through the process, animators suggesting sight gags, actors doing ad libs. All of this gets done sort of by consensus.''

The last rewrite comes after the actors have done a read-through rehearsal. ''We call it a table draft,'' Simon explains, ''because we get the actors around a big table and hear them read it through. That's our last chance to make big changes in the script, to see which scenes work, which ones need reworking, everybody getting a chance to pitch better jokes. It's something that's never been done on a cartoon show before.''

A few days later it's time to record.

The basement of the Darryl Zanuck Theatre, tucked away in a corner of the Twentieth Century Fox lot, is dark, with bare, green carpeting, a vaguely musty smell, and scratched-up tables and chairs. A coffeepot percolates against the back wall, next to an old, sagging sofa. This is where a Simpsons script comes to life.

In the center of the room, arranged in a circle, are a dozen reading stands holding scripts. Above each stand is a large microphone and a small lamp, just enough light for the scripts to be read, barely enough for the actors to see one another's faces. But faces don't matter much here. It's the voices that count.

Simon, Groening, and a battalion of writers and producers sit at a long table, facing the microphones. At the moment Dan Castellaneta, the voice of Homer Simpson, and Harry Shearer, playing Mr. Burns (Simpson's weasel of a boss), are rehearsing a scene in which Homer tries to convince Burns to run for governor.

''I think you really want to play up the discomfort of being stuck with your boss in an awkward situation,'' Simon says to Castellaneta.

''You mean,'' Castellaneta says, ''I'm really trying to suck up.''

''Exactly,'' Simon says.

The eerie thing about watching a Simpsons voice-over session is how much the actors resemble their characters. The cast includes Julie Kavner (Rhoda Morgenstern's younger sister on Rhoda and a featured regular on The Tracey Ullman Show) as Marge, Nancy Cartwright as Bart, Yeardley Smith as Lisa, and Shearer (a veteran of Saturday Night Live and This Is Spinal Tap) as practically everybody else.

As Castellaneta, another Ullman stalwart, reads Homer's lines, he acts out the scene, waving his arms, running in place, going slack-jawed and bug-eyed at all the right moments. Suddenly he is Homer Simpson.

''Sometimes the animators come to the voice-over sessions just to watch the actors and their gestures,'' Groening says. ''They get a lot of ideas about how to draw the scene.''

There are 34 scenes in this Simpsons episode (scheduled to be shown next season), 48 double-spaced pages of script. It will take the better part of a 12-hour day to record the dialogue. Although there's a team atmosphere, Simon is the man in charge, asking for take after take to get just the right nuance.

''I want less of a growl there,'' he says at one point, ''and more of a murmur.''

All day long, the actors go in and out of character, resting on the sofa between takes. Shearer falls asleep with a newspaper in his hand, snoring loudly until he's called to the microphone again.

He and Castellaneta start to improvise, making up dialogue they know will never be used. ''So, Simpson,'' Shearer says in his Mr. Burns voice, checking to see whether the producers are paying any attention. ''Have you ever had real hashish?''

Surrounded by drawings and charts in their office at the Klasky-Csupo animation house in Hollywood, two of the animation directors, David Silverman and Wesley Archer, are wearing the unofficial Simpsons team uniform, the clothing of choice for everyone from executive producers to production assistants: It consists of T-shirts, jeans, sneakers, and, if weather permits, a Simpsons letter jacket. Each jacket has a name embroidered on the front and Bart Simpson's distinctive head sewn onto the sleeve. The animation directors are trying to explain, as simply as possible, how the animation process works.

Be forewarned. This is where the math kicks in. ''We usually don't start working until after the dialogue is recorded,'' Silverman says. ''In the beginning we started working on storyboards based on the original scripts, but there were so many changes made that now we wait until we have the actual tape.''

Storyboards are the initial outline of the animation process, line drawings of the key scenes in each episode. ''It's not every acting moment,'' Silverman explains, ''but there's one drawing for every scene, like if you cut from a close-up to a wider shot. Generally there are 300 to 400 scenes per show.''

It is up to the episode's animation director, working with a storyboard artist, to decide how each scene looks. Although the scripts often come with general suggestions — such as ''a concerned look comes over his face'' — it's up to the directors to fill in the blanks.

Although Groening drew the original character designs, Archer and Silverman designed many of the secondary characters. Even Sam Simon gets involved in character design. He created the character called Bleeding Gums Murphy, a saxophone-playing drifter.

''The animation directors really are the style of the show,'' says Simon, ''and David Silverman in particular was the guy who created the visual style of the series. I'm continually amazed at how they take some of the milder scripts and turn them into great shows.''

Once Simon and Groening have approved the storyboards, the next animation step is layout drawings that serve as the blueprint. They're sent to Akom Animation in Seoul, where the actual animation is done. Layouts include drawings of every key movement in the show, whether it's Bart running across the schoolyard or Maggie blinking. There can be as few as 4 and as many as 30 layout drawings in a single scene.

''The more drawings we put in, the less written instructions we have to send along,'' Archer says.

Accompanying the layout drawings are detailed exposure sheets, which describe in words and pictures every frame of animation — everything the animators in Korea need to know. There are 24 frames for every second, 24 minutes in every show. The mechanics of a simple eye blink can take half a page of instructions.

Seventy members of the Klasky-Csupo animation staff in Los Angeles work full time on The Simpsons. For every show, at least eight people do layout drawings and whole departments design backgrounds and decide which colors to use in which scenes. Every detail is discussed and debated, including such matters as the color and shape of the Simpsons' kitchen radio.

''There is a certain look to the Simpsons' universe,'' Silverman explains. ''Everything's a little bit on the puffy side.''

Groening is as heavily involved in the animation process as he is in the writing and production. ''My style is not that easy to emulate,'' he says. ''And we had a rocky beginning, trying to draw the characters the way I designed them. It's very hard for people who devoted themselves to animated cartoons to break the habit of cuteness. My characters are anti-cute.''

The final step before the material gets sent across the Pacific Ocean is an animatic of the episode, a filming of the layout drawings that gives a rudimentary sense of how the show will move. There's no color and the movements are, at best, jerky, but the animatic gives the producers a chance to see how the drawings and voices work together.

''It gives the producers a chance to say, 'Maybe we need a close-up here,' things like that,'' Silverman says. ''It's a real luxury. As far as I know, no one else does this in TV animation.''

It takes the Klasky-Csupo animation staff 12 to 14 weeks to complete the storyboards, layouts, backgrounds, and animatics that are sent to Korea. It's six weeks more before the finished animation comes back. By the time Simon, Brooks, and Groening get their first real look at the show, the air date is less than three weeks away. And there's lots of work still to be done.

''This is my favorite part,'' Groening says. ''It's like going to a free concert.''

He's sitting in the control room at Fox's Sound Stage No. 1, listening to a 38-piece orchestra lay down the soundtrack for that week's episode. In a week that began with meetings and rewrite sessions, and would end with tedious hours going over sound effects and last-minute edits, here was an island of bliss.

Groening had no idea when he took the job that he'd be working 12-hour days, six-day weeks, immersed in this odd world. He still produces his ''Life in Hell'' strip, but admits he never gets to work on it until after midnight. ''But I never used to work on it until then anyway,'' he says. ''The difference was that I got to sleep in the next day. Now, I don't.''

As Richard Gibbs conducts the orchestra, Groening is clearly impressed by the force and intricacy of the pieces being played, impressed even more that it is music for a show he created — but not so impressed that he doesn't make suggestions.

''Could there be more of a flourish there,'' Groening says to Gibbs, ''something a little more majestic?''

''I guess I could be less involved,'' Groening says, ''but this really is a blast. I love every aspect of it and the closer we are to the final product, the more fun it gets.''

He talks with pride about the details of the show, subtleties that most people probably wouldn't notice. He knows there has never before been a cartoon TV show with a 38-piece orchestra, never been a show where scenes were rewritten after the animation process had begun, where actors were called back to re-cut dialogue, where people spend hours to get the right sound of a squealing tire or an angry mob.

Says Groening, happily, ''We knew when we began that the kinds of things we were attempting were extremely ambitious, trying to make people forget they were watching a cartoon, really getting them caught up with the characters. And we're succeeding.''