How does iOS 5 decide which home screen to put new icons on? I currently have an iPad running iOS 5. There are three home screens, which, for simplicity, I'll call A, B, and C. 

A has 7 apps and one folder.
B has 9 apps.
C has 10 apps, one folder, and newsstand (whether that's an app or a folder I don't know).

Whenever I install a new app from the app store, it installs on B. If I move a bunch of apps from C to B so B is full, the new app installs on C. 

It seems like apps will never install themselves on A. Is this correct?
Screen A that you refer to is the original 'Apple' home screen. Your observation is correct. The only time an app will install on screen A is when it is already present (or moved by you) and you are updating to a newer version of the app.

All other new apps will be installed in the screen closest to what you define as Screen A when possible (i.e. if Screen B is already full, it will go to screen C and so forth). New apps will never get installed into folders (unless you update the app that is already within a folder)