The back of your watch is attached in one of two ways. Look at the watch back. If it's smooth all around the circumference of the back, you have a snap-fit back. If, however, you see little notches cut into the edges--if they were extended, it would make the back look like a pizza that's been cut into slices--then you have a back that screws on and off.
A snap-fit case back often has a small (very small) raised section at one spot of the rim; this is so you can insert a tool called a case knife and pop the back off. If you don't see that small raised section, you'll need to wiggle the blade of your case knife under the edge and gently apply leverage from there--it's usually easiest by one of the watch lugs, as opposed to near the watch crown. If you don't have a case knife, you can often use a thin (but tough!) knife blade to do the same thing. Remember, though, that applying this much force through a knife blade can distort or take a chunk out of your edge, so be prepared to sacrifice a knife or be prepared to re-sharpen it after this exercise. A screwdriver does not work very well; the blades are typically too narrow to provide good leverage without distorting the case back, and they may even cutt a gouge into the watch body. Avoid using them for this purpose. To increase the water resistance of watches, Relic case backs are often very tightly fitted--they're tough to get off, and even tougher to push back into position. I would not be surprised if you would need a jeweler's press to get the back of this watch back into position.
If, on the other hand, you have a case back with notches in it, you will need to unscrew the back of the watch. You'll need a special wrench to do this. There are lots of makers and models from a basic $5 "watch crab" to a $100 workbench-mounted device that works on all kinds of watches, including Rolexes. Again, because screw backs are usually tightly fastened to increase water resistance, simply using a pair of needle-nose pliers in the ridges probably won't work. Nor will using a screwdriver in one notch--these backs are designed to move when equal pressure is applied around the edges, and applying force in one area only locks things up. Under no circumstances try to pry off the back if you have a screw back -- this will damage the threads, and you'll probably never be able to get the watch back together again.
You can find case knives and case wrenches at many jewelry supply stores, mail order supply houses like Otto Frei (http://www.ottofrei.com/store/home.php?cat=296
will take you right to the watch repair tools), and on eBay. However, if you're near a Harbor Freight store, they sell a "watch battery changing kit" and jeweler's press for an extremely reasonable price. These aren't the ultra-high quality tools that a professional jeweler would use, but they'll be perfectly fine for changing the occasional battery for many years. I've probably closed 100+ watches using the inexpensive press I got from there.