You are going to have to remove the battery to find out which one you need. For instructions on how to do this see: http://www.mademan.com/mm/fossil-watch-battery-replacement-guide.html. You can buy the battery at: http://shop.batterymart.com/search#w=fossil%20ch2599%20watch%20battery. Replacing a Fossil battery is delicate and tricky. Fossil recommends that you send it to a shop that specializes in Fossil watch battery replacements.
Take Watch to Watch shop for them to fit new battery .. As you don't have original battery in your watch, you would not what type to buy if you wanted to fit it yourself.
I have a Fossil and a Nixon watch that have very similar backs. Usually when it has those grooves all the way around, the back just screws off. I know they make some special tools to twist it, but I had luck with gently using some needle nose plyers.
Hope that helps and good luck.
Jerry, If its smooth on the back cover, you have to pry it off carefully. Get a magnifying glass and look around the cover edge, there should be a small under cut. Pry at this point with a penknife blade or similar. If the cover has 6 or 8 small indentations in it then it likely unscrews but you may still need to see a watch shop for the tool to unscrew it.
Fossil watches have a 2 year warranty so if its inside this, take it to a dealer.