Q: Is there some place that tells me the process of compiling Blender?
A: See the following documentation - http://wiki.blender.org/index.php/Dev:2.5/Doc/Building_Blender
Q: Where can I learn more about Blenders code base?
A: There is quite a bit of good documentation here - http://wiki.blender.org/index.php/Dev:2.5/Source
Q: The Blender code base is huge! Where do I start?
A: The editor directory is usually a good place - it is where most of the operators live. Have a look at the header files and structs related to what you are interested in working on. The headers usually have the best overview of what a function does. (To find the struct a simple grep or other search for struct FooStructIWantToLookAt will find it for ya.) You can also start with writing python scripts, the API for our python tools is similar in many ways to our C API. You can often find out where some C code lives by seeing the python tool tips by hovering over a button and seeing what the operator name is. Also if you add a console window you can see what is output to it when you do an action. Then just search the code. Also putting a break on a function in a debugger and doing a back trace can help you find the path code took to get to your function of interest.