It's no big deal.
The battery is a CR2032. It is one of those flat ones. You can get them just about anywhere they sell camera battery's. It is about the size of nickel.
To open the case you first have to remove the Key ring.
Then using a coin "use the biggest one the will fill the slot" to pry on the case. Start working from the notch at the top and go around both sides.
You will see after you open the case that the battery is seated in a metal frame just take it out and put the new one in the same way. "same side up as the old one". It works best if you mount the battery with it's case into the side that holds the battery then put the other half on top.
Snap the case back together starting at the bottom.:thumbs