As far as how to open up your drive, you could look online to see if there are any instructions. There should be screws and/or a release mechanism. Don't just rip it open if you want to be able to use it later without securing it with duct tape.
For your data's sake, I'd SERIOUSLY NOT TRY TO ACCESS IT ANYMORE OVER USB. If the drive is damaged, trying to access the data only makes it worse, and shortens your window of opportunity to get data off of it.
If you can get it out of the enclosure, and then connect as an internal drive in your computer, then it would probably be best to just use some recovery software to let it recover whatever you can get. One of the better ones is Active GetDataBack, Active File Recovery, Active Partition Recovery. There are also some others. I'd suggest looking for reviews to see which one you feel most comfortable with, and also determining whether or not you're willing to spend money to tray and recover the data.
If the data is really really valuable, and worth it, and you can't get to it, seemingly through these methods, there are professional data recovery services. However, if you have to go that route, be prepared to pay $1,000+ if they have to open up the drive itself.
"But thanks be to God, which giveth us the victory through our Lord Jesus Christ." 1 Corinthians 15:57