The best way is to download the whole project under your favorite IDE and use the IDE tools to gain a first overview.
For the Apache Software Foundation for example, they have just one huge Subversion root from which you can pull any single project in a few clicks using Eclipse. This creates a project in your workspace and you can use all the powerful tools of Eclipse to understand the class hierarchy, navigate (Ctrl/click) from one class to the next or just search artefacts in files. The same holds true for Intellij or Netbeans of course.
For github, just add a git plugin to Eclipse and do the same. At Sourceforge they use Subversion as well and used to rely on CVS, but the same will apply.
It seems like a lot of work but believe me it isn't. This strategy will also allow you to understand the various ways to build and architecture OSS (Maven, Hudson/Jenkins, Ant, make/nmake etc...).
Once you've done it once, it's much easier the second time and you'll find out it's always the same process.
Your developer skills will get a boost from taking this option seriously.