Fairly simple: The most common dual monitor configuration is the extended desktop. Essentially, your OS sees one large screen(the sum of the areas of your monitors) and windowed programs behave normally, as you would expect from moving them around on a single monitor. For full screen programs, the program in question occupies the entirety of one screen(typically the one selected as "Primary" during the setup. One thing to note is that, with some cards, the capabilities of the primary and secondary video out are asymmetric. For example, you may only be able to play video or use hardware 3d acceleration on the primary. This depends on card and driver, though.
Mouse cursor behavior is exactly what you would expect from using a single monitor, save that if you push the cursor to the edge of one screen, it will move over to the other. You get used to managing windows across two screens very quickly indeed. The only nuisance comes up when a program(many games are like this) grabs cursor focus. This prevents you from moving your cursor over to any other program. Say you are playing an FPS, for example, if you move your mouse over, your gun will track the pointer as normal; but you won't be able to leave the window. This is good for the game, and control would be a pain without it, but when you have dual monitors, you can see the chat window(or whatever other program) that you cannot access, which is a nuisance.
In conclusion. Try it, you'll like it. A Lot.