Richmond grew up in Portage County, Ohio, and graduated from James A. Garfield High School in Garrettsville, Ohio, class of 1979, where he won the John Philip Sousa award and where his mother still lives. He also played a key part in the creation of the Garrettsville Community Players, directing, choreographing, and lending his creative and artistic vision to many of its shows in its beginning. He attended Kent State University in Ohio in the late 1980s, where he co-authored a number of musicals, and wrote a musical score to william Shakespeare's Othello.

Richmond is married to Tina Fey, the creator and star of 30 Rock. They met for the very first time while working at The Second City and dated for seven years before marrying in a Greek Orthodox ceremony on June 3, 2001. They have two daughters, Alice Zenobia (born on September 10, 2005) and Penelope Athena (born August 10, 2011). His Father, Wayne Richmond, died in June 2014.

Richmond worked at The Second City and Child's Play Touring Theatre before he began composing music for the series Saturday Night Live. Richmond left SNL in 2006 to produce and compose music for the situation comedy 30 Rock. Richmond has also appeared as an extra on various occasions on 30 Rock, as the character Alfonso Disperioso; and, beginning in 2010, he directed five episodes: "Argus", "Plan B", "The Ballad of Kenneth Parcell", "Today You Are a Man", and "A Goon's Deed in a Weary World".

In 2008, Richmond composed the score to the film Baby Mama, which starred his wife, Tina Fey, opposite Amy Poehler.

Richmond is a recipient of the Child's Play Touring Theatre 2012 Victor Award.

Richmond wrote music for the Broadway stage adaptation of Mean Girls, which had it's out of town Broadway tryout in Washington, DC. The musical began previews on Broadway March 12th, 2018 and opened officially on Broadway on April 8, 2018.