I've been learning more and more about Android, and I've become interested in maybe trying to develop an app. What are some subjects I should study up on before doing so?
A similar discussion was brought up over at XDA. I can't post links right now becuase of my post count, but go here: forum.xda-developers(dot)com/showthread.php?t=685590p
If you are trying to get into app developement, I'd suggest going over the information on the Android website and learn Java to get you familiar with what is going on.
If you want a full understanding you can start by studying some of these broader subjects like a Computer Engineering college curriculum would cover:
Operating Systems, Databases, Networking, Programming Design, Programming Languages, etc.
For the quick and dirty:
Linux and Java and find all the source code you can get your hands on!!!