You should really take it to a jeweler that offers this service. there are special tools made to remove the backs, and you can scratch the case (or worse) if you remove it incorrectly. Most places only charge about 5.00.
I have never replaced a watch battery myself. We always take ours to the jewelry/watch repair place in the mall. For the cost of the battery, they do the work. (I think they have the correct tools and know what they're doing - which I do not.)
Taking it into a jeweler or to the watch store you bought it from is the best idea. Some watches have special tools used to remove the backs. I have tried going to walmart before, but they did not have the tool needed for my watch. We took it to a watch store that sells my watch brand. This was a good thing because it turned out the battery wasn't dead, but some internal part was bad (have forgotten what it was) and that normally it would cost about $15 plus you would have to send the watch away. Just so happened that they had one part that was for my watch model, put it in for me and changed the battery all in one stop and all for only $15!!
I guess I'm in the minority here. I just grab a pocket knife and pry the back off myself. It's usually not that tough to do. It'll only cost you a few buck to have it done at the mall, but don't be afraid to try it yourself. Unless the watch was expensive.