As a senior at St. Anthony High School, Martin was a Parade First-Team All-American and named to the McDonald's High School All-American team.
Martin received a full scholarship from UCLA and played on a Bruins squad with future NBA players Don MacLean, Tracy Murray and Mitchell Butler. As a quick point guard, he completed his college career at UCLA in 1992 ranked second in school history in both assists (636) and steals (179) behind Jerome "Pooh" Richardson. His career assists total placed him fourth on the Pacific-10 Conference's all-time list. Darrick averaged 9.3 points and 4.9 assists in his four years at UCLA. As a junior, he averaged a career-high 11.6 points and 6.8 assists, and his assists average was the best in the Pac-10 and the 16th highest in the country. His single-season high of 217 assists was second all-time at UCLA to Jerome "Pooh" Richardson's 236.
The 5'11" point guard was not drafted by an NBA franchise and instead played for the CBA's Sioux Falls Skyforce, (where he was the league's 10th leading scorer with 21 points per game) prior to signing two consecutive 10-day contracts with the NBA's Minnesota Timberwolves in February 1995. He returned to the Timberwolves for the 2003–04 NBA season as a backup for Sam Cassell after Troy Hudson was injured.
At the beginning of the 1995–96 NBA season he signed with the Vancouver Grizzlies as a free agent, but the Grizzlies traded him back to the Timberwolves two months later, in exchange for a second-round draft pick. His scoring average in these first two seasons remained at about seven points per game.
Martin signed with the Los Angeles Clippers in 1996 and remained with them for three seasons, averaging ten points per game in (and playing all 82 games of) the first two of them.
He returned to the Clippers in the 2004–05 season and averaged 3.8 PPG.
Martin's contract expired once again after the lockout-shortened 1999 season, and he signed with Sacramento Kings where he would spend the next two years. Late in the Kings' 130–109 win over the Dallas Mavericks on March 6, 2000, Martin came off the bench to score 11 points in only two minutes. He was given the nickname "The Domino" by his teammates.
Martin signed with the Toronto Raptors for the 2005–06 season. In his first year with the club he posted 2.6 ppg and 1.4 apg in 8.5 mpg of play. Martin's primary role with the Raptors, according to head coach Sam Mitchell, was to provide guidance to the younger players on the team such as point guards T. J. Ford and José Calderón. Darrick's most notable moment in a Raptors uniform was a 3-pointer against the Dallas Mavericks on November 29, 2006. With over a second remaining in regulation, and the Raptors trailing by 22 points, Martin hoisted up a 3-point shot uncontested and successfully sunk the shot. With the Raptors NBA record consecutive game streak with a 3-pointer on the verge of ending, Martin's shot enabled the Raptors to extend the streak which ended January 24, 2011. After two and a half seasons with Toronto, Martin was waived on March 27, 2008, to open up a spot on the roster for Linton Johnson. Though waived by the Raptors, Martin stayed with the team as an informal assistant coach/consultant.
In November 2009, Martin returned to his first NBA team, the Minnesota Timberwolves, as the assistant director of player development.
In 2012, Martin was named an assistant coach of the St. John's Red Storm men's basketball team, working under head coach Steve Lavin.
On October 27, 2015 it was announced that he had been hired as the Play-By-Play Voice of the UCLA Bruins on the UCLA Bruins IMG Sports network, replacing Tracy Murray.
On June 22, 2016, Martin was named the head coach of the Reno Bighorns of the NBA Development League.