If your paint is scratched and you want to fix it not just hide it, you need to machine polish off the top layer of scratched clearcoat/paint. This is a lot easier than most people think but you do need the right gear.
Here's a video that runs you through a full 2 step polish, for most cases you will only need a 1 step which is the same process just with different pads.
Clean and clay before polishing, if there are waxes glazes etc on the paint you want to remove these first with wax stripping soap cleanslate or a really strong mix of citrus wash and gloss soap.
Once you have polished lock it in with either and easy shine kit from earlier, or a Ceramic Kit.
2 Step Polish On Really Bad Paint
A Note On Pads
As you polish your pads are removing clearcoat/paint which gets into the pad, the pads backing plate and polishing machine get hot, and the pads get clogged.
By the time you have done 1/4 to 1/3 of a car you should stop and swap pads. If you keep going to try and do the whole car with the same pad you will get poor results as the pads are no longer cutting like they should, and they will be too hot.
Thats why these kits only give you a choice of 3 or 4 pads. The also include pad conditioner, pad cleaner and a pad cleaning brush. Most kits don't include these or have so many pads but you really need them.
You should clean your pads the same day and leave them to dry at least overnight either face down or standing up so the water drains and doesn't sit on top of the valcro. Its easy to clean them and important to do it the same day or the polish can dry inside the pad foam itself creating hard spots that reduce the life of the pad and can damage your paint.
These kits give all you what you need.
What About Ceramics
Ceramics are pretty cool, and you'll see a lot from us about them.
Ceramics need to go directly onto cleaned, clayed and ideally machine polished clearcoat/paint to properly bond to the surface.
You can put glazes, sealants, waxes on top of ceramics, but putting ceramics on top of glazes sealant waxes will mean they can't bond to the paint so won't last.
There are trade-offs in ceramics of longevity vs ease and speed of use:
Carbon Force will last up to 5+ years but you need to make sure you apply it properly and its very important to prepare the surface properly.
Hydroslick lasts up to a year and applies super easy like a wax,
Hydrospeed is super quick and easy spray and wipe, and will last a few months but is super easy to apply.