PVC is easy to patch, but here are a few tips:
Make sure to buy pressure type PVC and fittings, (DWV type fittings are shallower, cheaper, and designed for drain pipes).
For wet conditions you want to use the Blue type PVC cement labeled rain & shine, it will cure underwater, just be aware the working time is only a couple of seconds in hot weather, so coat the parts and stick together quickly.
For best results use a primer (either purple or clear), purple is the most common, but stains and is messy, it is required in some job sites where inspectors need to confirm primer was used, otherwise it is the same stuff.
When the damage is in a length of straight pipe, special telescoping repair fittings are available, these cost more than basic fittings, but are much quicker and easier to use. ($20-25 vs $5-7 in typical pool size pipe fittings). The hardest part is working in a mid section and having enough flexure of the line to get the couplings over both ends, often you will be forced to use a union fitting the screws apart in the middle (but requires accurate pipe length cuts), of an easier to work with, but more expensive telescoping fitting.
Ike
p.s. there are probably a lot of how to patch pvc pipe videos on youtube (it really is simple, cut out section with hack saw and replace with an assortment of fittings and pipes (elbows, couplers, threaded or slip fit, etc.)