Woods started to play basketball at a young age, and as a sophomore in high school he was already 6 ft 10 in tall and a key member of the varsity team.

[1][2] Coached by Bobby Joe Perry, Woods averaged 16.8 points and recorded 439 rebounds in his sophomore year[3] and he was named MVP of his district.

[1] Several college coaches regarded him the best big man in the nation,[7][8] and in his 3 years of varsity basketball at Bryan High School he won 3 championships in a row.

[9] He also played in another high school all-star game, the Capital Classic, where he scored 16 points (7/9 shooting, 2/3 on free throws).

[10] Woods was heavily recruited during his high school career, and received interest from Texas A&M, Michigan, USC, Kentucky,[6] Hawaii, North Carolina[7] and LSU.

[17] Since Texas A&M won the SWC conference title, they participated in the NCAA Tournament, where they were eliminated by Louisville in the Midwest Regional semifinals.

[15] During his time at Texas A&M he was part of "The Wall", a group of players noted for their defensive prowess, along with David Britton, Claude Riley, Vernon Smith and Rynn Wright.

[2] After his final college season, Woods was automatically eligible for the 1982 NBA draft: the Dallas Mavericks selected him with the 4th pick of the 4th round (73rd overall).

He initially signed with the Wisconsin Flyers, and in the second part of the season he transferred to the Lancaster Lightning, where he also played during the playoffs, averaging 20.3 points and 8.0 rebounds per game.