What you need:
- A clean, rinsed car
- Paint cleaner
- Microfibre cloth
Prior to polishing check whether the paint feels smooth or maybe still has some rough patches. In case of rough patches pre-treat the paint with a paint cleaner.
Apply the paint cleaner using a soft sponge in a circular motion, and then work it in using a microfibre cloth, again in a circular motion.
Before polishing give the car a proper rinse. This calls for absolute thoroughness because any kind of dirt can scratch the paint during the polishing. Also make sure to park your car in the shade to ensure best results.