How to replace a watch battery?
That back cover on your watch is a press fit into the main frame of the watch body. 

The typical way these are removed is to place a sharp blade along the side groove where the cover meets the body. Most times the cover actually hangs over the body some toward the outside and placing pressure on the sharp blade will start to make the cover pull up from the body a small amount. Continued work around the perimeter will eventually get enough of a space between the cover and the body that you can get a small flat blade screw driver in the space to twist and get the cover fully free. 

Reassembly is a process of just pressing the cover back in place. You want to make sure to squeeze it into place evenly all the way around so it goes in straight. If the cover is cocked off at an angle it could bind in the body and not seat all the way in.