Richard was born in Vevey. At the start of his career, he was a successful cyclo-cross cyclist, becoming world champion in this discipline in 1988. Later on, he switched to road-cycling, and showed a considerable talent for climbing. He won the classics Giro di Lombardia in 1993 and Liège–Bastogne–Liège in 1996. In 1996 he also gained Olympic gold after winning a sprint in a successful three-man breakaway in the men's road race.