I have changed the battery
The case-backs on some snap-fit watches are very snug in order to increase the sweat and water resistance of the watch. That means that you may need a case press in order to get the back put in place again.
Before you go heading off for a case press, check a few things first. Look carefully at the case back. On some cases, there's a cut-out for the set stem. Is that properly lined up with the stem? If not, that will prevent that case from closing. Next, look for evidence of a thin neoprene gasket that might be either around the case back or lying between the case and the case back. Is that properly in place? Even a little bit of gasket getting in the way will make it really hard to close the case back.
However, I'm guessing that you need a case vise--or that you'll have to give someone with the proper wrench a few dollars to close up your watch. Putting the watch in a regular vise and squeezing tight is a very fast way to wreck your watch--there's a very high risk of cracking the crystal, deforming the case back, or even putting too much pressure on the interior movement and damaging it. A case press puts pressure only on the outside of the crystal bezel and on the edges of the case back--flexing the parts that need to get flexed, but sparing the rest of the watch from that kind of pressure.
Case closing vises come in two basic flavors. The first, which I prefer, is a little tool that sits on a table. You fit in appropriate nylon collars, put the watch between them, and push down with a lever. The second, which I find doesn't always work, looks more like a set of salad tongs with a strange end (actually, parallel pressure points). With this tool, you also add appropriate inserts, then squeeze the handles together like a pair of scissors. It doesn't exert as much pressure as the table-mounted tool, but it's often enough.
Jewelry supply stores carry these case presses, but if you are near a Harbor Freight hardware, store, they also carry inexpensive versions of both of these case presses for a very reasonable $10-15. However, you can usually find someone to close your watch up for you for even less.
Good luck!
