Braun coached Siena Heights for eight years, taking the National Association of Intercollegiate Athletics (NAIA) school to a 148–103 record and five postseason tournaments.
Prior to the 1985–86 season, Braun took on the position of associate head coach at Eastern Michigan.
During his 11 years at Eastern Michigan, he guided the Eagles to four postseason berths, including three NCAA appearances.
The team finished the season 23–9 and gave Braun a school record for most wins by a Bear coach in his first year with the program.
Then after entering the NIT, the Bears, led by Geno Carlisle, won five consecutive postseason games to capture the NIT title – Cal's first postseason tournament championship since the Bears won the 1959 NCAA title.
In 2000–01, the Bears returned to the NCAA Tournament, finishing with a 20–11 record, and Sean Lampley – Braun's first recruit at Cal after NCAA sanctions were lifted from Bozeman's tenure – became the school's all-time leading scorer late in his senior campaign, finishing with 1,776 points.
In 2002–03, Cal again reached the second round of the NCAA Tournament behind All-Pac-10 forwards Joe Shipp and Amit Tamir.
On November 21, 2005, Cal defeated Long Beach State, 88–69, to give Braun his 500th career win.
After losing to Ohio State in the 2008 National Invitation Tournament, Braun was fired as head coach of the Golden Bears on March 26.
Braun was hired as the head men's coach at Rice, replacing Willis Wilson in 2008.