The House approved legislation yesterday to authorize about $28.5 billion to improve the nation's airports and air traffic control system, a measure made overwhelmingly popular by recent airline passenger complaints.

"It's up to us to take action that will make the system work again," Rep. James J. Howard (D-N.J.), chairman of the Public Works and Transportation Committee, said before the House approved the bill, 396 to 0.

The measure, sent to the Senate, authorizes spending $8.6 billion for airport improvements and construction, $9.3 billion to modernize the air traffic control system, $9.5 billion to pay part of the salaries of air traffic controllers and other federal aviation workers and $1 billion for research and other programs over five years.

For fiscal 1988, which began yesterday, it authorizes spending about $4.9 billion for aviation projects, about a one-third increase over the $3.7 billion provided last year. The bulk of the increase is in spending for airport improvements, which would grow from $1 billion in 1987 to $1.7 billion this year.

The money would have to be provided in later appropriations bills. Congress has not passed spending bills for the new fiscal year.

Authority for the programs financed in the legislation expired Wednesday night, but congressional aides said that, even without the new bill, money will continue flowing for several weeks.

The bill would also renew special taxes that pay for much of the government's aviation projects. These include an 8 percent tax on airline tickets, a $3 fee on overseas tickets and levies on aircraft fuel and air-shipped cargo. That money accumulates in the aviation trust fund.

By a 202-to-197 vote, the lawmakers refused to remove the trust fund from constraints of the overall federal budget.

Supporters have said $5.6 billion has accumulated in the fund because of a desire to make the federal deficit appear smaller. Taking the money off budget would eliminate that temptation to not spend the money, they said.

But opponents argued that the money was not spent because the equipment it was to purchase was not available. Removing the fund from the budget would simply mean that other programs would have to be cut more deeply when Congress approves deficit reduction spending slashes, they said.

The Reagan administration has threatened to veto the legislation for several reasons, including insistence that the $8.6 billion in airport grants be reduced to $5.1 billion.

Under the legislation, about $170 million would be spent annually on airport noise-reduction programs, some of which would be distributed to public schools and hospitals for soundproofing materials.

The bill also orders the Transportation Department to conduct a two-year study of how the nation's air traffic system can be expected to grow through the year 2010 and to submit recommendations on how to handle the increase.

The lawmakers voted, 385 to 14, to continue a program that provides subsidies to airlines serving about 150 small communities in 40 states. Supporters argue that, without the subsidies, the carriers would lose money on many of the routes and abandon them.

On a voice vote, the lawmakers added a provision that would make unauthorized removal of debris from the site of an airline crash a felony, punishable by as many as 10 years in prison and a $250,000 fine. The crime is now a misdemeanor.