Sham has been with the Cowboys since 1976, when he was hired to be their color analyst alongside play-by-play man Verne Lundquist. Sham also held the position of Sports Director at former Cowboys Radio Network flagship station 1080 AM KRLD between 1976 and 1981. When Lundquist left for CBS in 1984, Sham became the lead play-by-play man, a position he has held ever since (save for three seasons in the mid-1990s). In 2003, Sham wrote Dallas Cowboys: Colorful Tales of America's Greatest Teams (ISBN0762727594). He also contributes weekly columns to dallascowboys.com. The 2009 season marked Sham's 30th year with the organization; the longest of any broadcaster with the team, albeit not consecutive due to his three-year absence from the club from 1995 to 1997. During his absence from the Cowboys, Sham called Texas Rangers games on the radio with Eric Nadel between 1995 and 1997.
Sham has done NFL play-by-play for the NFL on Westwood One, the NFL on Fox, TNT Sunday Night Football, and the NFL on CBS for one game in 2004. He has also worked games for NFL Europe and the Arena Football League's Dallas Desperados. Sham has extensive experience broadcasting collegiate sports, having done play-by-play for NCAA athletics, most notably the NCAA Men's Division I Basketball Championship and college football. He spent over a decade as the radio voice of the Texas Longhorns' football and basketball teams (mostly in the 1980s), which also aired on flagship KRLD and on the Mutual Southwest Radio Network. Sham has been in the booth for 26 Cotton Bowl Classics, calling play-by-play for 25 games and serving as the analyst for one. He has also served as a play-by-play broadcaster for the Big 12 Network basketball Saturdays, as well as for select ESPN Network Big 12 games.