A few things could be going on here, first a few questions:
- Does the hard drive "spin up"?
- Does the computer make any noises or have any balloons popping up in the bottom right corner?
- Have you tried another USB port (silly question, but great for Googlers!)?
If you get either of the first two, you will want to try right clicking on "My Computer" and selecting "manage". From there, you can select "Disk Management" from the left hand side and see if your disk is listed among those available in the lower-pane. If it is there, right click it and select "Assign Drive Letter and Path" and give it a drive letter.
If you don't get a "spin up", then the drive is most likely not receiving enough power from the computer. If this is a desktop, make sure you are using some USB ports on the back connected to the motherboard itself and not those infront of the computer where less power can be drawn. If this is a laptop, try other ports and specifically look for an eSata port (doesn't look like a USB but you can still put a USB in there), a blue/red USB port, or a USB port that has a small lightning bolt on the case next to it's identification mark. All of these types of ports should provide marginally more power.
Of course, you may want to also ensure that your hard drive works in the first place. Make sure that you try it on another computer before you spend all evening beating up your laptop!
Hope this helps.