I'm trying to get the mouse's position on the screen and not the game, but I've looked at the API reference and I can't find anything related to this. Any help would be appreciated!
Try this:
http://wiki.roblox.com/index.php?title=API:Class/UserInputService/GetMouseLocation
Alternatively, these also exist, but I wouldn't use them:
http://wiki.roblox.com/index.php?title=API:Class/Mouse/X
http://wiki.roblox.com/index.php?title=API:Class/Mouse/Y