Wash and Polish
It’s an arduous undertaking, as you only work on a very small area at a time, but the results can be spectacular. Clay bars are made of a special compound that, when lubricated and worked over a panel, will pick you near microscopic amounts of dirt and grime that has become embedded into the paint.
The trick to using a clay bar is to keep it well lubricated and fold it often. Don’t work it too much without re-moulding it in your hands, otherwise you just end up working the dirt back into the paint.
If there are still swirls and scratches, another idea would be to machine polish the car. You’ll need the car to be washed, dry and free of other polish products. Then, once you’ve acquired a machine polished from your local car place, you can start polishing.
Start with a fine grade cutting compound, put a few dabs on the pad, then set the machine to its lowest setting and work the compound in. When it’s evenly dispersed, up the speed and work the compound in further.
You DO NOT need to press the machine into the paint; it just needs to be the lightest touch - the weight of the machine itself, if that.
And when the compound starts to ball up, that’s enough. Buff it off and then apply final polish. It’ll be well twinkly.