Three cheap tools from a well-known online retailer named after a river.
The middle one I found to be almost useless. It is the style used by some professionals but they probably use much better quality versions and have more skill than I do.
The right hand one is excellent, works for all but one of my watches with press-fit backs (not that I have many).
I bought the left hand one for a troublesome Tissot. It worked perfectly.
Press-fit backs generally have, somewhere around the perimeter, an area with a slightly larger gap (or a gap rather than none). Sometimes barely perceptible. You insert the sharp hard edge of your tool there and lever the back off.
For refitting the back, I find a watch press useful:
Though any soft-faced vice would probably work if you are careful. The advantage of the above item is that it doesn't exert pressure on the glass/crystal front of the watch and so doesn't risk cracking it.
There will be a gasket. Make sure it is in the right place or it will be impossible to refit the back. On my Tissot the gasket was left in the case when removing the back but to replace the back I had to first fit the gasket to the back, not to the case. Other watches will vary considerably.
Although some of these tools cost less a cup of coffee at a coffee shop, they might seem expensive compared to the cost of a Yazole, so you'll have to make a choice based on how many battery changes you expect to do in future.