I first try to familiarize myself with the high level design/org of the code base, going through the README, other docs, looking at the test code if any and just generally scanning the important files/modules etc.

Then I prefer to jump into fixing any existing issue. Working on fixing an issue teaches a lot, more fixes, then features, rinse, lather, repeat.

While this post talks about fixing compiler bugs, the overall steps are much replicable: http://random-state.net/log/3522555395.html