Many modern clocks have a small battery-driven quartz movement fixed to the back of the dial. If you turn the clock over you'll probably see a small plastic box about 50mm square and about 15mm deep, holding an AA (LR6) battery, which lasts a year - see Image 1. Some older battery clocks predate quartz and have electro-mechanical movements with a visible balance and hairpring powered by a larger battery (MN14 or LR14). Either way, the movement is probably be held in place with a thin brass nut on the front of the dial like one of the three illustrated in Image 2. If not, then it probably has three tiny screws underneath the dial. Some also have a hanger underneath to carry a light pendulum (Image 3) and some strike and chime through a detached loudspeaker mounted in the clock case (Image 4).
Compared to clockwork movements, they are inexpensive; they can also be more reliable and durable but they vary in quality and specification; hands have different size/shape holes for fixing, some push on and some screw on. Shaft lengths also vary enormously. German ones by UTS (Uhren Technik Schwarzwald) are still among the best despite a decision to move production to China because it's largely a question of good design and quality control.
Small clocks might have a different type of quartz movement which is set into the front in one self-contained unit and takes a smaller LR1 battery (Image 5). These are common in china clocks like those from Aynsley, Coalport, Masons, Royal Doulton, Wedgwood etc and glass clocks by Caithness, Swarovski and Waterford etc. Replacing the unit will probably cost less than £50 but if you need to have the same dial (bearing the maker's name), you'll need to let me have the old movement so that I can make a replica and that will add £12 to the cost.
If your quartz clock has stopped, first check that the hands are not coming into contact as they pass one another, or dragging against the surface of the dial. The hands are delicate and often unprotected so they can easily get damaged or bent. They can also be straightened easily, too. If they're OK, try a new battery (fitted the right way round!) but AVOID Duracell batteries (especially in older movements and Chinese ones) as they seem to have too high an output that can upset the vibrations of the quartz crystal.
If that doesn't work, don't bother trying to strip it down to find the cause; I now have a fast 'swap-out' service dedicated to replacing quartz movements. I'll re-use the existing hands if they can be adapted to suit the new movement so that the clock will look exactly the same afterwards but it's not always possible because shaft sizes and shapes vary from one make to another. Where I do have to fit new hands, I match the existing ones as closely as I can.
Prices start at £45 for the simplest type including fitting, which might take only 48 hours. Of course, if your clock has a swinging pendulum, or chimes and strikes, or has a radio link to the nuclear clock station, it will be more expensive.
I don't make a habit of replacing old mechanical movements with new quartz ones because that compromises the clock's integrity and originality. But the 'proper' repair of some lesser clocks of low intrinsic value has uneconomic cost implications and I completely understand that. So rather than see a vintage clock being thrown away because of the unaffordable cost of repair, I will look at whether a quartz movement is a viable alternative.
All paid for work's guaranteed for a year.
If your modern clock doesn't have a battery but is driven by weights or springs that you have to wind up every week, then take a look at my separate page on modern mechanical clocks for repair options.