The trick to successful polishing is to use the appropriate abrasive material reducing in grit size (increasing fineness) and only move onto a finer abrasive once all of the 'scratches' from the previously used abrasive material have been removed. This can often most easily be achieved by applying the abrasive at right angles (90 deg.) to the previous operation, this will show up any previous 'scratches' that need to be removed. The quality of the final finish will depend on the fineness of the final abrasive and whether all of the previous marks have been removed.
Polishing plastic can be achieved by initially using silicon carbide paper (wet and dry) increasing in fineness from 600 to 1200 to 2400 to 3000. This can be done by hand but must be done wet with plenty of water, the abrading action generates heat which will cause the plastic to soften and 'drag' you can then finish off with something like Duraglit or even T-Cut. You can get specialist compounds for the final polish, 3M do one as well as Meguiars.
If you use a machine polisher for the final polish use a slow speed and avoid too much pressure, the generation of heat during this process can be a disaster.
My next 'How To' will be based around teaching Grandmas to suck eggs.

Nich.