Trinidad was born in Los Angeles, California. In the early 1980s, he was one of a group of poets who were active at the Beyond Baroque Literary/Arts Center in Venice, California. Other members of this group included Dennis Cooper, Bob Flanagan, and Amy Gerstler. As editor of Sherwood Press, he published books by Cooper, Flanagan, Gerstler, Tim Dlugos, Alice Notley, and others. In 1988, Trinidad relocated to New York City. He received his Master of Fine Arts from Brooklyn College in 1990. He taught at Rutgers University, the New School, and Princeton University. His collection Plasticville (2000) was a finalist for the Lenore Marshall Poetry Prize of the Academy of American Poets. In 2002, Trinidad moved to Chicago to teach at Columbia College Chicago, where he co-founded the literary journal Court Green. His personal papers are archived at Fales Library at New York University.

In addition to his own books of poetry, Trinidad has edited Powerless, the selected poems of Tim Dlugos (1996), Holding Our Own: The Selected Poems of Ann Stanford (with Maxine Scates, 2001), and Saints of Hysteria: A Half-Century of Collaborative American Poetry (with Denise Duhamel and Maureen Seaton, 2007).