Skinner was drafted by the Vancouver Canucks 68th overall in the 3rd round of the 2002 NHL Entry Draft. Brett was a member of the Trail Smoke Eaters in the BCHL in 2000–01, the Des Moines Buccaneers in the USHL in 2001–02, and then the University of Denver from 2002–2005. As a Denver Pioneer, he was a member of two NCAA national championship winning teams, was named an All-American in 2004–05. He was named team captain for what would have been his senior year at Denver (2005–06) but signed his first professional contract with the Canucks on August 30, 2005, and made his pro debut with affiliate, the Manitoba Moose of the AHL, in the 2005–06 season. At the trade deadline, Skinner was traded by the Canucks, along with a 2nd round pick to the Mighty Ducks of Anaheim for Keith Carney and Juha Alen on March 9, 2006. Despite being dealt, Skinner remained on loan with the Moose until the end of the season.