It wasn't something that happened overnight - it's a process that really started in 1989 with Gorbachev's political reforms that began to decentralize power in the USSR, and picked up speed rapidly in 1991, especially after the failed August 19,1991 coup against him, and Boris Yeltsin's "counter-coup" shortly after.

Some links for more information: an answer I wrote on Gorbachev's generally-perceived role in the dissolution, an answer on the 1991 coup attempt against him. Here is an answer as to what happened to the Communist Party, here is one about what happened to the Soviet military and security forces, and here is a description of the economy and material conditions during the collapse.