As pointed out by Section 107, few climb MP itself. Huayna Picchu is another thing entirely, and, as mentioned, tickets are much tougher to come by. It's quite an arduous climb and even tougher descent; if I recall correctly, plan on a 3 hour round trip for that alone. But there are plenty of other trails that are interesting and not quite so arduous (and would extend the time you need past 3 hours). Inca Bridge and Sun Gate, for example.

Just keep in mind it's a tough haul if you want to really explore. Bring lots of water and some food!