HOW DOES A young artist get from nowhere to the National Gallery? Or to lunch with Joan Mondale? Or on the cover of Newsweek? In fact, how does an artist get anywhere since, according to the Bureau of Labor Statistics, there are 183,000 painters and sculptors at work in the U.S. today?

One way is to go through Washington's Big Art Machine -- the second largest in the country. Although it is not absolutely necessary for success, many of the area's estimated 6,000 artists have to rely on it.

To qualify for a Big Art Machine, which takes in unknown artists and disgorges celebrities, a city needs collectors, critics, museums and -- most important, money, the oil that keeps the big wheels and little cogs turning. Washington now has, though in unfortunately disproportionate amounts, all of these elements, and is still growing.

Here is how the system works.

Getting a Dealer

The gallery system as we know it didn't get under way in America until 1838, when John Herring opened the Apollo Gallery on Broadway in New York. After discovering that hanging art on the wall was not enough to lure viewers (a discovery some Washington dealers have not yet made), he invited the public to subscribe at $5 per year to "The Apollo Association," promising each member an engraving and a lottery ticket for an "original" painting.

This was the first public acknowledgement that buying art in America was basically a gamble, and proof that collectors preferred it that way.In 1844 the Association gave away 450 paintings, realizing a total take of $40,907, and the first American art machine had begun to chug.

It is still important for an artist to get an imaginative, resourceful dealer who will earn his half of your income by organizing shows, placing works in important private collections and getting them accepted into the best museums. Some dealers may eventually offer an artist an annual stipend, but the volume of sales in Washington does not often make that possible.

Best of all, of course, is a cult dealer like New York's Leo Castelli, since collectors with money but no taste like to stand in line for their works of art, secure in the knowledge that if everyone is waiting in line for something, it must be good -- or at least a good investment.

That notion may leave art-lovers cold, but then art-lovers rarely have the money to buy art.

Because there are no cult dealers in Washington since the depature of Max Protetch, now of 57th Street in New York, the next best bet might be the new idealists, a whole new generation of young dealers devoted, they insist, "to helping unknown Washington artists." Some, like Jack Rasmussen, actually do seem willing to make a marginal living helping unheralded artists of this city in whom they strongly believe. Franz Bader has been doing the same thing for years. There are others, including Louis Andre, Diane Brown and the well-capitalized Middendorf/Lane gallery, which hedges its bets by selling early 20th-century American masters.

Other possibilities include a number of artist-run alternative spaces funded by the National Endowment for the Arts, which along with the better co-ops have helped provide some machinery which did not exist before the '70s. They have taken the sneer off many a dealer's face.

Alternatives notwithstanding, most artists still will not make it through the Big Art Machine: There are too many artists and too few spaces.

In simple arithmetic, there are now close to 150 galleries in Washington showing art on a regular basis. Assuming that each organizes 10 shows a year, 1,500 slots are theoretically open to new artists. That means that 4,500 area artists are excluded right off.

But of the 1,500 slots, only about half are open to new artists, since most galleries repeat their big sellers each year, reducing possibilities to roughly 750.

And because of Washington's new importance as an art center, there is stiff competition from artists of national and international reputation, including big names from Paris (and the past) like Bernard Buffet and Yaacov Agam, along with American bigwigs like Jasper Johns and Helen Frankenthaler. That cuts the possibilities down by half again, to perhaps 375 slots. Get one of those, and you're on your way.

Maybe. Dealers, no matter what they say, are not masochists. If you sell, they'll give you another show; if not, you'll probably be dropped. Dealers are in business to make money. And, come to think of it, so are you... if you like to eat.

"Nobody can afford to be an artist without independent means, a job or a rich mistress," says artist Patrick Ireland, who has a job at the National Endowment for the Arts. "Art as a mistress has a very cold bottom."

If all else fails, have an affair with a dealer, but be sure it's a good one.

Getting Reviewed

"It doesn't matter what you say as long as you say something," says Barbara Fendrick, summing up the importance of reviews. Her gallery, like most of the others, presses hard to get them.

In fact, early reviews -- often one-liners like "promising" or "one to watch" -- are used chiefly as coupons which can be traded in for another show or a grant, which might lead to a museum show, ensuring another review. The critic, therefore, becomes a small but important cog in the art machine.

Again, good dealers are important because critics assume that they know a good thing when they see one. Their recommended shows, therefore, are usually checked out. Schlocky dealers and dilettantes usually get one visit from a critic, and that's it. When artists complain that critics keep visiting the same galleries, ignoring the rest, they're often right.

There are, however, fine outlying galleries like Plum Gallery in Kensington, Gallery 4 in Alexandria and others that don't get covered routinely. Fair or not, it helps to be in town.

Never underestimate luck as a major factor in reviews. One artist got a bonanza because a newspaper used the wrong photograph to illustrate a review -- in fact, it used a work by an artist the critic had given a bad review. The painting was sold over the phone next morning, sight unseen. Praying for such a windfall isn't a bad idea.

If all else fails, have an affair with a critic, preferably a good one.

Getting a Patron

After getting a dealer and a review, you'll need collectors and patrons. A pushy mother or mate can be a big asset at this point. They will harass anyone you like, organize special showings, and keep critics apprised of your every coup. (Do not, under any circumstances, marry another artist, unless it is a very rich one who is no competition for you.) A rich patron with good and powerful connections is invaluable. In addition to buying your work, a patron can throw large parties in Georgetown -- maybe even a dance or two -- for other potential buyers, dealers and critics.

If you are young and attractive, the task becomes at once simpler and more complex. You may never know whether the patron loves your art or you, but fair is fair: Your patron, likewise, will never know whether you love him or his money.

Incidentally, next time you take out a loan to buy groceries, get chummy with the president of your bank. Banks are spending large amounts of money buying art and organizing shows. As dealers repeatedly point out, there are only a handful of real collectors in Washington, so be resourceful. Corporate offices, lawyers, dentists and doctors are all buying art at a great rate, so woo them all.

If all else fails, have an affair with a corporate art patron, preferably a nice one.

Getting a Grant

Grants help in getting fame and fortune. They also help in getting more grants. Which is how many artists now survive -- for a year at least.

Though amounts are small ($3,000 to $10,000 -- at the National Endowment for the Arts), they help attract other support. With an NEA grant, a museum show becomes a real possibility, and vice versa. After all, every taxpayer will not have a real stake in your future.

But it isn't easy. In fiscal 1978, there were 6,000 applications for NEA fellowships, but only 3.4 percent could be funded, given a budget of $1.3 million. NEA hopes to double fellowships grants by 1980, so hang in there.

Getting a Legend

A myth is as good as a mile in the art world. If you aren't basically very interesting, and your art less so, you'd do well to get yourself a legend and stick with it.

While you strive to look good on paper, strive to look bad in public. Drive an old VW bus and wear something outrageous, or at least remarkably different.

Mark di Suvero, for example, is always the grubbiest person in any crowd. Carl Andre, similarly, costumes himself in carpenter's overalls, though his look is rather '60s-passe. Chambray work shirts are still in, but Dior scarves worn with them are out. Turtlenecks are in. Jeans are out, except for work. Corduroys are in, the more rumpled, the better. (The artist who can get Walter Hopps to part with his corduroy jacket will have it made.)

For more dramatic impact, you can move to New York, and then announce to the press that you've left because no attention was paid to you here. What a headline: "Ignored Washington Artist Leaves Washington!" National art journals like "Art in America" will take notice of you for the first, but possibly the last, time.

Meanwhile, be sure to keep your teaching job at the Corcoran or at the University of Maryland, and spend at least three days a week here earning a living and preparing for your next show -- in a Washington gallery.

Or, for notoriety, you might do a huge outdoor mural of a reclining female in a bikini -- the bikini done with paint that will wash off with the next rain. When the first drops fall, call the press. They'll send a photographer right over.

Repression and obscenity are big news, and you might organize an exhibition and arrange to have it closed by the police because someone phoned in to say it was pornographic. The advantage of a trial should not be overlooked. Have Robert Rauschenberg and others take out an ad in leading newspapers appealing for contributions to your defense fund. Settle out of court and keep the cash.

Interior decorating is another ploy that always works if you cannot get reviewed, and a pad in SoHo with an indoor swimming pool is a good bet. Ask Lowell Nesbitt.

You can also go to New York with another up-and-coming artist, visit Helen Frankenthaler, and return to Washington transformed. It didn't work for Morris Louis or Ken Noland right away, but everything takes time. Frankenthaler has not yet begun charging for this service, but anything is possible -- so don't wait.

If all else fails, have an affair with a legend, preferably someone powerful in the arts.

Getting in a Museum

Having come this far, the next step is a museum and the chance for immortality.

To prime the pump, a good dealer will already have made a gift of your work, if a sale was not possible. Or perhaps a donor can be found to purchase a work (at a big discount) and donate it (at full market value) to a museum, giving the donor a fat income tax deduction. The importance of taxes, and the reduction thereof, cannot be underestimated as a factor in the donation of works of art to museums. The laws were so designed. Learn them.

After becoming a tax dodge, there is nowhere to go but up, to the big museum show. Or at least that's what's supposed to happen, though many artists, to their astonishment, have found themselves turned away at this point.

Having an affair with a curator could work as a last-ditch effort. But most of them know better. And by this time, you're likely to be too old and too tired.

(Suicide at this point is not a bad idea, though not a new one. Posthumous celebrity is celebrity, however unsatisfying.)

But assuming, optimistically, that the big museum show finally comes at the NCFA or the Hirshhorn or at the Modern in New York: You've made it! You're on the "Today" show, collectors are scrambling for your works, critics begging for interviews, and curators protecting you from the press. It can only be topped by the invitation to dine at the White House with Leonard Bernstein, Louise Nevelson, Andy Warhol and Jamie Wyeth. Lunch with Joan Mondale was more fun, but let's face it: Being a big star makes the whole terrible struggle almost worth-while.

At this point, buy a tux with rubber pockets, so you can steal soup and canapes for the kids back home, who still have to eat. Fame, it turns out, doesn't guarantee fortune at all. After burning bright for a few years, and being asked to speak (free) to every age group in town, and to donate your works (free) to every charitable cause in sight, you may well find out why so many celebrities are broke.

Once noticed, it is important to stay noticed, and you may have to spend the rest of your life doing just that. Some artists, like Frank Stella, seem to have no trouble exploding with new ideas. Most, however, fade into oblivion, resurrected only in their obituaries to perplexed readers who assumed the artists were long since dead.

So stick with a style as long as it sells -- but when it stops selling, get yourself another gimmick fast. Then the reviewers can say, "despite the great success this artist has had with the 'X' phase of her work, she has moved on, out of esthetic necessity, to another phase -- proving that mere success is not her goal."

If all else fails, get Nelson Rockefeller to make a reproduction of one of your works, and you can watch them selling like hotcakes, just past the lingerie at Neiman-Marcus.