bridging?

I am thinking about buying 2 or 3 subs to put into my car, but I was wondering if I could wire them all to one amp and save some money. I heard this is called bridging. If so, how would that work. I am either going to get 3 10 inch subs or 2 12 inch subs. The 10 inch subs run 500 watt RMS (on the box anyway) and the 12's run 800 watt RMS so either way I go I would just like to know if I could use one amp to power all of the subs.

This will really depend on the subs that you have. I would recommend contacting a local dealer in your area so that they can help you with your decision and plan your system according to your budget. Let them show you what they can do for you.
To your topic though, depending on the final impedance of the subs there should be no problem running a single amp.
Bridging is combining 2 channels of an amp into 1. If you are running subs, generally you are going to be running a MONO (single) or DUAL (2) channel amp. It works the same way with the Voice Coils of the sub woofer. Some subs have single, dual, or even more. There are different ways to bridge woofers but only 1 way to bridge an amp and that is to follow the directions for that amp. It generally is the Negative from 1 channel and the Positive from another. You can learn more by searching this site.

"Bridging" an amp usually refers to combine two or more channels to produce a single larger one. You must be careful not to create a load too low for the amp to handle because a bridged amp will operate at 1/2 of what the speakers' total impedance is. In other words, a 4-Ohm speaker connected to a bridged amp loads the amp to 2 Ohms. If you put two 4-Ohm speakers in parallel and connect to a bridged amp, it will be 1 Ohm.