One of the most common reasons for a pump to stop working is a broken impeller or blocked impeller. Impellers are the only moving part in your pond pump and for this reason they are the most likely part to need some maintenance.
***Make sure the pump is unplugged
A broken or blocked impeller is by far the most common reason for a pond pump to stop working and fortunately is also the easiest to fix. Accessing your pump's impeller can vary from brand to brand but it is generally a similar processs and is fairly easy for anybody to do.
First remove the pump cage and/or any pre filters sponge which is covering the inlet of the pump. Some pumps have a large plastic cage with round or square holes that covers the whole thing - this can simply be removed. Other types have a smaller cage, often with a sponge underneath that can usually pull or unclip off of the pump. Beneath this sponge and/or cage there will be an impeller cover. With some pumps you need a screwdriver but with most of them it is a simple quarter turn 'bayonet' type cover which can be removed without any tools. Beneath this cover you will see the top of the impeller (looks kind of like the blades on a boat propeller).
Once you have the cover off you will need to remove the impeller. Sometimes you can grab the top of it and pull is straight out, other times you may need the assistance of a pair of pliers. If using tools, be very careful as most impellers have plastic blades which will snap easily if pressure is applied at the wrong angle. It may be necessary to clear or flush some debris out of the way before you can remove the impeller. The impeller sits on a shaft which is usually removable as well and has a magnetic rotor connected to the blades which is also on the shaft.
If the impeller was blocked with debris, simply flush and clear out the impeller chamber as thoroughly as you can removing all dirt, sticks or other foreign objects. You can them reassemble the pump and it should work.
It is also possible that the impeller or shaft is broken. You will easily see if the shaft is broken as it will be in 2 or more pieces. Regarding the impeller, if the plastic blades are separated from the magnet and can be pulled completely apart, then it is broken and the impeller needs replacing. It may be possible that the impeller is still attached to the magnet but not properly. To check this, hold the magnet in one hand and the blades in the other hand and try to turn them in the opposite direction. Most impellers will turn slightly and then lock. If the blade keeps spinning on the magnet without ever locking, then your impeller is broken and needs to be replaced.