As his 15-month quest for the presidency headed into its final days, independent Dennis Serrette laughed as he recalled how it all began.

"I woke up one morning," Serrette said, "and fell out of the wrong side of bed."

Serrette, 44, a black switchman for a New York phone company, had been active for a number of years in the labor movement, especially with a coalition of black trade unionists.

He was first approached by two independent parties about running for president.

"I said, 'Run? Run for what?' " Serrette recalled. "And they said, 'Run for president.' I said, 'Are you kidding?' "

They weren't, and Serrette has been on the campaign trail ever since. Despite obstacles, Serrette will be on the ballot in 33 states, including the District of Columbia and Maryland, and is conducting a write-in campaign in eight others, including Virginia.

Independent groups supporting Serrette's candidacy include the United Citizen's Party of South Carolina, the Liberty Union Party of Vermont, the Labor and Farm Party in Wisconsin and the Alliance Party in New York.

Nancy Ross, a teacher, is Serrette's running mate. Together, they hope to use Election Day as a "day of protest" against both major parties, which they say "do not address the problems of black and poor people in this country or the problems of war."

Serrette has visited homeless people in San Francisco and white senior citizens in Gary, Ind., and Philadelphia. "This is really an American tragedy, to see these people who have given so much to America," Serrette said.

Though his campaign began four months before Jesse L. Jackson's, Serrette now refers to his coalition of small independent parties as the Rainbow Alliance. His platform calls for full employment, a national health plan, affirmative action, fair housing and no first use of nuclear weapons.

He said the campaigns of Walter F. Mondale and President Reagan are virtually indistinguishable. "Mondale is going after the same vote that Reagan is, the conservative white vote," Serrette said.

Serrette planned to end his campaign in Jackson, Miss., then return to his job at the phone company.

Would he run again? "If I got the calling to do it again," Serrette said. "But I'm not too anxious to run and jump into the pool tomorrow."