In 1956, Buechner received his bachelor's degree in political science from the College of Wooster.
Buechner received his master's degree in public administration from the University of Michigan, in 1958, and then received his doctorate degree in political science, in 1963, from the University of Michigan.
Buechner served in the Colorado House of Representatives in 1973 and 1974 and was a Republican.
In 1995, Buechner served as chancellor of the University of Colorado Denver campus.
From 1995 to 2000, Buechner served as the 18th president of the University of Colorado system.