With the number of concerts and pro and college sporting events that are held in the Los Angeles area, they already had enough venues to handle most Olympic events. They only had to build something like two new venues (a swim center and a velodrome, I think).

They used student housing at a UCLA (and USC?) for Olympic Village. That had plenty of capacity because a lot of students go home during the summer break.

Basically, the Olympics wasn't a lot more than Los Angeles normally handles, so I'm not surprised it went off well.