Originally posted by: MRGOOCH
There is some kind of clip on the edge. How do you operate it?
Whatever you do, do not pry it back very far. It will break and you're SOL if that happens.
Gently pry the clip slightly upward a fraction, using a tiny screwdriver or something similar and pop out the battery. It's usually a two-handed operation, but can be done with one if you're good.

Just take your time and be careful not to pry back the little clip back too far.
Another thing to remember is you will lose all your settings in the BIOS when you do this. It's usually a good idea to write them down before doing the replacement so that you can set them back later.