Find a clean area to work, with good light.
First make sure the button for adjusting the hands is pushed in, if it was out the watch will not work.
If your watch has a bracelet, it is easer if you remove the pin that joins the too halves of the strap and that is used for adjustment, so you can easily get to the back of the watch (these pins are spring loaded so be careful).
Have a close look around the edge of the back to see if there is a small slot to get a pen-knife in, to pries the back off.
On cheaper watches, what looks like a screw back are just push on, so check for a slot.
Screw backs can be unscrewed if you haven’t got the right tool, by putting two 3mm drills in a vice the correct distance apart or by using something similar.
When you’ve got the back off, be very careful not to touch the coil with any tools, as the wire is much thinner than a human hair. Most batteries are towards the edge of the watch, so keep a finger between the battery and the movement, in case a tool slips.
Make a note of which way the battery is fitted, 95% have the + and the battery number to the top.
Some batteries are held in place with a flat spring plate with a screw or screws; the spring usually has a slot at both ends not holes. Just loosen the screw next to the small hole in the spring, then fit a pointed tool into the hole and slide it across, (be careful it is a spring).
Do not use metal tweezers to hold a new battery and avoid greasy hands.
When putting the back on the watch, do not press on the glass if it is a flat one, as it will crack, only press on the outer edge or place it on a clean hard flat surface with a single tissue between.