Though the opening ceremony doesn't begin for another day, today has already seen the start of qualification in the men's and women's slopestyle snowboarding, and in a little bit, women's moguls and the first parts of the new team figure skating competition.
Sochi is nine hours ahead, so it can be tough to keep track of what's when. I'll suggest the official Olympic site, NBC's Olympic site, and my personal favorite, this interactive Olympic calendar at Sports Interaction which offers both schedules and results.
NBC's full TV schedule is here. Sadly, nothing until primetime today, but all events will be streamed online.