Why did versus populum (the priest facing the congregation) become commonplace after Vatican II, when ad orientem ("facing east," with the priest's back to the congregation) was the norm before Vatican II? Did a Vatican II document prescribe versus populum?
No Vatican II document said that priests must face "toward the people" (versus populum). In fact, all Masses today can be celebrated ad orientem ("toward the east," the same direction the people face, which is toward the tabernacle).
During the aftermath of Vatican II, Otto Nussbaum's study, which concluded that versus populum was the norm in the first four centuries of Christianity (although this is disputed), influenced many modernists today who want to return Christianity to its "primitive roots." Versus populum is also in accord with Vatican II's relative anthropocentrism.
Missale Romanum (2002), Institutio Generalis no 299:
‘Altare exstruatur a pariete seiunctum, ut facile circumiri et in eo celebration versus populum peragi possit, quod expedit ubicumque possibile sit.’ (‘Let the main altar be constructed separate from the wall so that one can easily walk around the altar and celebrate facing the people—which is desirable wherever possible.’
‘Quod’ (‘which is’) naturally refers to the first clause of the sentence, not the second, which is subordinate to it. See C.M. Cullen and J.W. Koterski ‘The New IGMR and Mass versus populum’ Homiletic and Pastoral Review June 2001 pp51-54.