Fairfax County yesterday requested proposals from cable television firms that want an exclusive franchise in the county, ending more than three years of study and opening a bidding war for what will be the most lucrative contract the county has ever awarded.

Twenty-four firms, many of them with influential lawyers and former politicians to represent them, have expressed interest in providing multichannel service to Fairfax. With its population of 600,000 and median family income of more than $33,000, the county offers cable companies one of the most tempting franchises in the nation -- estimated to be worth $260 million 15 years from now.

The Board of Supervisors' unanimous vote yesterday brings Fairfax in line with Washington's other suburbs, which either have awarded franchises or are within months of doing so. The District of Columbia, which also is planning a cable TV system, has not progressed as far.

Fairfax cable administrator William Rossi says he expects the board to finish evaluating all proposals and award its franchise by July 1, with construction starting no later than the summer of 1983. The winning firm will have to provide cable service throughout the 400-square mile-county within five years of starting construction, under the terms of the proposal approved yesterday.

That 298-page document demands detailed information on applicants' ownership and financial resources, the number of channels and type of programs they will offer, the two-way communication their system will make possible and the facilities they will provide for community programming. County officials hope the bulk and detail of the data they are requesting will help them avoid problems like those in Arlington, where officials have accused the cable firm of not fulfilling all its promises, or in Alexandria, where the franchisee recently said it was losing so much money it will have to sell out.

How difficult that may be was illustrated when a nationally known consultant abruptly stopped advising Fairfax County last week and charged that its request for proposals is seriously flawed. The board shrugged off the criticism yesterday and hired a new consultant to evaluate the proposals, at a cost of$8,000 per proposal.