As above Len, Ideally you should use a variable speed rotary polishing machine, well worth investing in, and will last you forever! Use 1500 or 2000 wet/dry with a little washing up liquid and plenty of fresh water, just a gentle rub, removing nibs in the paint, and deal with any orange peel, but not so much that you rub through the lacquer, and hit the base!... this will require re painting, so easy does it..
polishing mop head should be clean, and saturated with water (if the foam type) the excess water squeezed out, using the mop damp, will help stop heat building up, and less likely to damage the fresh paint...
Use Farecla G3 cutting compound (a good all rounder) a small amount applied to the mop head, and not the panel should work well, and not make too much mess, a marble size amount of G3 is sufficient for about 12sq inch,
Once you're happy with the compounding, wash the panel thoroughly clean of any remaining G3
You're now ready to finish the polishing process, using a anti hologram polish (3M's is excellent, though a little pricey) re polish the freshly painted area, using a specific polishing head (lambswool is ideal) do the rest of the car while you're at it! clear residue from you're paintwork, and wax at will...
HTH
Thom
