Sam was born June 1, 1985 in Washington, D.C. The eldest of five children, Young was born to single mother who supported her family by working as a cable TV installer and moved often. By the time Young was in high school, the family had found its way to Prince George's County, Maryland. Young led his team to Maryland state titles in 2003 and 2004.
After graduating from high school, Young attended Hargrave Military Academy for a year, averaging 23 points and 11 rebounds for a team that went 28–1 and was ranked second nationally among prep school programs. The basketball recruiting site Scout.com named Young its National Prep School Player of the Year for 2005. He would decide to sign with the University of Pittsburgh.
Young joined the Pitt basketball team for the 2005–2006 season. In his junior year, Sam averaged 18 points per game, was named the 2008 Big East Tournament MVP after scoring 80 points in the tournament, and was also named the conference's most improved player. In his senior season at Pitt, Young averaged 19.2 points per game, and was given the honor of being a Third Team All-America. His 2009 NBA draft stock also increased after his spectacular performance in the 2009 NCAA Tournament in which he averaged 23.5 points in four games. He also received accolades from his opposition; Connecticut coach Jim Calhoun, who saw Young score 56 points in two games against his team in Young's senior season, including 31 on Pitt's 2009 Senior Day, said, "There hasn't ever been a player who gives us as many problems as he does."
Drafted by the Memphis Grizzlies in 2009, he is one of the most athletic players in the NBA.
Away from the basketball court, Sam writes poetry; he has spoken with a publisher about compiling his works. He is also a skilled piano player.