Just reading source won't improve your skills all that much. You might learn a trick here and there, but on the whole, changing the code will teach you far more than reading it ever will.
I would recommend finding an open source project that you like and use, identifying a few bugs that you are interested in fixing (finding bugs should be pretty easy, and if you can't do it yourself, check the bug tracker), and then fix them. Some bugs may be harder to fix than others, which is why I suggest finding a few different bugs; if you get stuck on one, move on to another. You will have read plenty of code in order to find the bug, and you will have thought the code through enough to be able to fix a bug in it. Furthermore, you will have improved a piece of software that you know and use, and if you submit the patch back to the project, you may get good review and criticism on your patch, as well as helping out future users and getting something to stick on your resume.