These first 2 pictures show some very deep scratches that are to deep to be removed by hand.
These next 2 pictures show a technique called wet sanding.
This is a highly skilled process which involves sanding the damaged area with various grades of sand paper to remove the damage which is then followed by various stages of machine polishing.
These last 3 pictures show the damaged areas after the sanding and polishing stages have been completed. This process can save you hundreds of pounds on a vehicle re-spray.