When playing Skyrim I am unable to move to my second monitor. When I move my cursor to the edge of the screen it doesn't move over, as if I were only playing with one screen.

Skyrim locks itself as the active program. In order to move the cursor to the other screen, or to other programs open on either screen, you'll have to open the console using the tilde key, and then alt-tab to another program or screen. And when you're finished, alt-tab back to Skyrim and close the console - because if you just click back into Skyrim with the mouse, you'll wind up with two cursors - the Skyrim one, and the windows one.

Now, if you're not on a windows PC, the above is likely not germane to your situation.

DirectX locks you to one screen. All games do that, at least if there is one that doesn't I've yet to find it.