Problem: Hard to move mouse, or movement does not translate well to screen.
Diagnosis 1: Mouse ball is probably dirty.
Solution: Start by flipping the mouse over. Usually there is a type of ring which you can turn and remove. Take the mouse ball out and wipe it off. Check the inside of the mouse; there is probably dirt or lint on the contact points where the mouse rolls. These can be cleaned off with a napkin (if your fingers are small enough) or a q-tip. Once you have cleaned it off, put the mouse back together, and try it again.
Diagnosis 2: Mouse pad dirty, warped, or worn.
Solution: Try using the mouse on different flat surfaces (A stack of papers, the top of a book, something like that). If it works better, the problem may be a dirty or worn out mouse pad. In this case, clean off the mouse pad, or request a replacement.

Problem: No response to mouse movement on-screen.
Diagnosis 1: Mouse disconnected.
Solution: Check the back of the machine and make sure the mouse is plugged in. Also, make sure it is plugged into the correct port. On newer machines, the mouse and the keyboard use the same type of port, so it is possible to mix them up (you can verify this by checking to see if the keyboard works). Also, check the integrity of the mouse cord.
Diagnosis 2: Program locked up.
Solution: Wait a moment to see if mouse movement returns. Check to see if there is any response from the computer to keyboard commands. It is possible to momentarily lose mouse input if the computer is under a heavy load, but it shouldn't happen often for a very long time.