Depends on the make of the watch; some watches have backings that pop off with using a sharp object and some watches have backings that are taken off by unscrewing counter-clockwise.
The one's that pop off usually have an area where you can insert a flat blade and pop off.
The one's that are unscrewed have notches around the edges of the back plate.
Well its quite simple to change a watch battery, with the help of a sharp object lift the rear section of the watch, this will expose the machinery where the battery fits, you will have to simply lift the battery up check for the negative and positive nodes of the batter and fix the new one.
A watch batter better known as a button cell basically is a minute form-factor battery created for use in things like wrist watches, pocket calculators, hearing aids, and identical compact electronic products.
Watch batteries are normally single cell with an ostensible voltage varying between 1.5 V and 3.0V. Normal anode substances are zinc and lithium, normal cathode substances are manganese dioxide, silver oxide, carbon monofluoride and copper oxide.