The District of Columbia's Commission on the Arts and Humanities will receive a $200,000 grant from the National Endowment for the Arts to help teach business skills to 24 local arts groups, as well as to instruct neighborhood organizations such as churches and schools in the fine art of ticket selling, advertising and other details of organizing a production.

Backers hope it will help shore up the typically precarious foundations of the city's struggling arts groups, reverse the flow of Washington performing artists to New York and nurture black performing arts groups.

"What do we do about these young, energetic arts groups?" said James Backas, executive director of the commission. "We know they're good. If they could only hang around for a few years, they might be able to get the necessary underpinning."

At a press conference at the District Building yesterday, NEA Chairman Frank Hodsoll, joined by Mayor Marion Barry, council member Polly Shackleton (D-Ward 3) and Backas, said that the federal money was a "challenge grant" that would be combined with more than $540,000 in newly appropriated city funds.

The federal largess is part of a 3-year-old endowment plan, written but not used during the Carter administration, that the Reagan administration hopes will catalyze local support of the arts.

Washington is one of 12 cities selected to receive NEA funds in the coming year, and according to Backas, the city's plan has been constructed to attack two of the most difficult problems for local arts groups: learning managerial and fund-raising skills while operating on a shoestring budget, and finding audiences in neighborhoods that more established music, theater and dance groups pass by.

"The small emerging groups really have a terrible time of it," Backas said. "They really don't have any organizational stability. They tend to put all of their money into what you see on stage, and they are constantly on the verge of disaster."

According to Backas, a lack of adminstrative know-how and fund-raising ability often prove the downfall of struggling arts groups. This has meant a notable lack of established black performing arts groups in a city where the majority population is black. "There is not even one medium-sized performing arts company in this city that is a minority company," Backas said.

Another result, he said, has been the cultural impoverishment of Washington as talented performing artists and companies leave the city.

A "terrible example" of that, he said, was the loss several years ago of Robert Hooks, a Washingtonian who in 1970 founded the D.C. Black Repertory Company, which folded six years later. Hooks left Washington to join the Negro Ensemble Company in New York City.

"We've lost some, and we're in danger of losing more," Backas said, citing the perennially tenuous financial straits of noted Washington artists such as choreographer Liz Lerman and Carla Perlo, director of the Dance Place in Adams-Morgan.

Other cities slated to receive endowment money include Chicago; Poughkeepsie, N.Y.; New Haven, Conn.; Dayton, Ohio; Jackson, Miss.; San Diego, and Seattle, all of which submitted proposals and will get between $150,000 and $245,000 each. Their proposals were as diverse as commissioning works for city festivals and finding audiences in culturally impoverished neighborhoods.

In Washington, eligibility will be restricted to groups with annual operating budgets of no more than $150,000. The first stages of the selection process have begun and will continue through the end of the month. The commission will use management consultants and a panel of experts to choose the eight organizations that will receive the grants each year.

The D.C. arts commission awarded nearly $800,000 in federal and local money to District artists and performing groups last year, but the money was awarded for artistic rather than administrative purposes.

The endowment's plan is similar to one drafted by Backas seven years ago, when he was assistant to Nancy Hanks, chairman of the arts endowment under the Nixon and Ford administrations. It languished for seven years, Backas said yesterday, a victim of changing administrations and a reluctance to give local governments too high a profile in a federal program.

The plan was dusted off by the Reagan administration, whose revisions included reducing the federal pot from $20 million to about $4 million.

Backas praised Hodsoll yesterday for undertaking a new federal program in times of budgetary restraint. Barry was equally enthusiastic. "We're on our way to taking the title of art and cultural capital of the world from New York and bringing it to Washington," he said.