I have an electromagnetic powered off a AA battery. Is there some kind of dimmer switch or similar item that would allow me to control the amount of power going to the electromagnet?
Yes, you can control the amount of power going to your electromagnet by hooking a rheostat in series with the battery and electromagnet.
Of course you could buy a rheostat, but if your primary goal is to learn you can make one. Here is a nice tutorial explaining how make a rheostat. Just substitute your electromagnet for the light bulb shown.