If it's 4 games in one day, you will receive 3 tickets. Two for Thursday which will be session 1 and session 2. Saturday will be session 3.
Session 1 is for the first two games of the day. They clear out the arena and then you have to re-enter with your session 2 tickets. Session 3 is two games on Saturday. They don't clear out the arena between games.
What used to be the opening round (round of 64) is a great day. You see some top notch teams and a cinderella. The fans get behind the underdog no matter who it is, unless they are playing the home squad. I suggest you try to buy tickets from one of the schools that will be playing. You'll have to pick up tickets via will call but you'll get better seats and face value. You can always check ticket master but you'll pay all kind of fees and the seats typically aren't that great.
I've done this for every NCAA Tournament game I have ever attended and by far it's the best route to go. You can try to upgrade your seats with scalpers outside but I've never had a bad seat coming straight from the university. The trick is to get tickets from a smaller school that is doing the furthest travel because they rarely sell out their allotment and will be glad to sell to you alumni or not.
Bring lots of money with you as well, it's a long day and you'll get hungry and thirsty. Plus get a cool NCAA Tournament shirt, one that has all the teams logos on it is a great one to have.