I am a fresh college grad student that just started my job. In my ramp up period, I need to learn a lot of product code. There are some design docs but they do not help much. >
Some people will tell you to start with the data structures, but in a large system even that's not terribly helpful much of the time. I can think of four major points:
Take your time. Often, it's more like a whole series of gestalt shifts than it is a single, linear, gradual understanding. So be patient.
No matter how big it is, you should be able to put a breakpoint in and walk it in a debugger. Even in a large, complicated, multi-threaded system, you should be able walk through and see what's happening.
Ask for bugs, and start fixing them, no matter how crazy they seem. It's akin to dropping yourself into a foreign country; you'll pickup the language eventually.
Find a mentor. A jungle guide is invaluable.