Create an account on github. Follow the instructions in the sticky post on how to create a pull request, but stop at the point where you work on the code. Then take a bit to look over the organization of the code generally. See that it uses Boost, see that most of the core code is one directory. The net code is in net.cpp, the RPC code is in rpc.cpp, and so on.
Then look through the list of bug reports on github:
https://github.com/bitcoin/bitcoin/issues?sort=created&direction=desc&state=openSee if anything moves you.
