Hello,
Many people who know more than me are going to recommend resurfacing rather than painting. They are probably right, but if you are like me and stuck with a painted pool, Ill tell you what I learned when I rehabbed my pool. Assuming your pool was previously painted you need to find out what type of paint is on it. It is probably best to send a paint chip off to lab to be sure, but you can get a few solvents to do a home test. For example xylene will dissolve rubber based paints. Then you should choose a paint that is compatible with your current paint. (Under most circumstances this means painting with the same type of paint) I called the manufacturer of my chosen paint and was told to get a glossy finish they said it contained less fillers and more resins. Glossy is also easy to clean and a little less prone to hold onto algae, but its certainly does not prohibit its growth. Follow the directions of your chosen paint exactly, the manufacturer also told me that the most common reason their paint fails is that people refill the pool before the paint has a chance to cure. If you are repainting with the same color with an the original paint in good physical shape then you should only really need one coat. It was easier and faster to paint the pool then I imagined. However make sure that painting is the right choice for you. I have no idea how long my paint will last I am hoping 3-5 years, which is not long but I can repaint my pool 20 times for the price of a resurfacing so it was the right choice for me. If I had bare plaster or concrete and need 3-4 coats I would not have choose to paint. Good Luck!!