If there drive spins up, then there's a good chance that it's the board on the back that's failed. If you can get an identical drive (ebay is often good), you can try swapping the boards over, which might let you read from then current drive.
If you've got very important data on it, and don't have backups, I'd advise taking it to a professional, trying to do it yourself with no experience will probably just end up destroying any chance of getting your data back.
Get a SATA-USB adapter. That way you can fiddle with it all you want. Boot into a Linux live-cd first, it will probably give you much more info than Windows -- try "dmesg" to see what the kernel has to say.
There are some software packages that are not free but are worth it you can get to do recovery. They work on the basis that reading some sectors off the drive may still work, so the software is smart enough to know by reading the sectors if its a word doc or an mp3 ect. and put the file back together (although you have to go through the nightmare of re-naming everything as filenames are lost)
They're useful if the drive is from a desktop or laptop & your worried about getting pictures & word documents off there. The two i have used with some success have been ZAR and OnTrack
I've had success with EasyRecovery Pro but this does assume that you can get the hardware up and running as mentioned in other posts. Any drive that I'm asked to look at that's at risk, I image first with Acronis True Image. But once again, assumes the hardware is working.
If the BIOS can't see it, replace the circuit board with one from an identical hard-drive.
If the platters don't spin up, you may have to rotate it quickly about it's axis to break it free of any grease that may have gelled up.
you may be able to get some data off of it by placing it inside of a freezer, and attempt to retrieve data off of the hard-drive, starting with the most important data first.
Run SpinRite on it to attempt to repair any failing sectors.
If you still can't get anything off of it, you probably are going to have to send it off to someplace that specializes in retrieving data off of failing hard-drives, but there is no guarantee that they will be able to get anything off of it either.