The Recovery Process
After you've connected your hard drive to a computer's USB ports, open "My Computer" and take a look at the list of drives; if your drive appears, you're in luck - that is, you have a better chance of recovering the lost files - and if it doesn't appear, then you'll have to try something else.
If The Hard Drive Does Appear: All you really need to do is download and run a recovery tool such as REMO Recover. This will search your hard drive for the hidden or deleted files, locate the problem within the drive, and then do its best to fix it so you can get your stuff off of it. Another great application (and the one I personally prefer) is PC Inspector which, unlike REMO, is completely free of charge. What you need to do after downloading it is simple: Open the application, run the recovery tool, and then select the drive you want to recover. Let it do its thing, and when it's done, you should be able to access the files normally.
If The Hard Drive Doesn't Appear: If your drive isn't even showing up after you've connected it, the first thing you should do it make sure your connection is solid. There should be no scratches in cords you're using, and no problems with connecting in the past. If you're sure it's properly connected, once again run the aforementioned "PC Inspector", but this time select "Find Lost Drive." This should look long and hard for your drive, eventually find it, do its best to recover your files and, ultimately, get your stuff back in total working order.
There are many other tools you can use to recover hard drives, of course, but many of them cost money and are a lot harder to use than other programs.