Be aware that the most time-intensive option is to sand your entire car's paint down, smooth it with sand paper and repaint the entire thing. If your car's paint is completely peeling and you would prefer not taking it to a car shop, this may be the best option. It is risky to do it yourself if you have not done it before, and an entire new paint job is only necessary if the car's paint is peeling all over, not just in a few small areas.
Touch up the peeling area as a good short-term solution. This is the best option if the paint is peeling in only a small, concentrated area. It won't look great from close up, but from a distance it will do fine. Don't apply a lot of touch-up paint to your car all over, because it is a temporary fix if your car's paint is peeling all over.
Take the car to a car shop that can professionally repaint it. This is the best and safest option, but costs the most money. This may not be necessary if the paint is not peeling all over the car, but if your car's paint is peeling all over, this is the best long-term option.
Paint over the peeling paint. This is not recommended but is cheap and does not take long, especially if your car's paint is only peeling in a concentrated area. The problem is that painting over it is a temporary fix, and the paint job will show the multiple layers of paint. This is only a good option if you do not have time to repaint the entire car or cannot afford to take it to a shop.