Drafted in the second round, 43rd overall by the Montreal Canadiens in the 1991 NHL Entry Draft, Craig Darby played two years of NCAA hockey before turning professional. While at Providence College, Darby became a well-rounded hockey player with excellent defensive skills. In his first season at Providence College, he had 41 points on 17 goals and 24 assists in 35 games in 1991-92. The following year he also appeared in 35 games, where he had eleven goals and 21 assists for 32 points in 35 games.
In 1993, at the age of 21, Darby joined the farm team of the Montreal Canadiens, the Fredericton Canadiens of the AHL. In his first season, Darby dressed for 66 games, scoring 23 goals and 33 assists for 56 points in 66 games. He followed that up by scoring 68 points in 64 games the following year. This point production, combined with a strong defensive game, prompted interest from some NHL teams. In 1994-95 he suited up for ten games with the Canadiens, picking up a pair of assists. Late in the season he was sent to the New York Islanders in a trade with Kirk Muller and Mathieu Schneider, and he dressed for three games on the Island. Montreal received Pierre Turgeon and Vladimir Malakhov in return. His Islanders career lasted another ten games into the 1995-96 season, but the bulk of his year was spent with the Worcester IceCats of the AHL where he played in 68 games, scoring 22 goals and 28 assists for 50 points.
Darby was claimed on waivers by the Philadelphia Flyers on June 4, 1996 and played in 12 games over two rather forgettable seasons. Darby returned to the Montreal Canadiens in 1999-00 and spent three seasons in the Habs organization while spending some time with the team's AHL affiliate in Quebec City before joining the New Jersey Devils organization in 2002-03. Upon his arrival with the Devils, Darby spent most of his playing time with the team's AHL affiliate in Albany before being acquired by the Tampa Bay Lightning in the summer of 2004.