Thing you have to remember is its a waste of time polishing paintwork that is not free from contaminents or debris , washing a car only removes the surface crap , if you polish straight on to this all you do is push the contaminents into the paint work which produces scratches and swirling.
Best thing you can do is clay bar or use a paint cleasner first , you will be amazed what this can do to your paint work.
and the thing people seem to forget about is waxing the polishing you have just done , this protects and seals (depending if you use a synthetic or natural wax).
great results can be achieved but you have to remember its not a one hit wonder that you just do and forget about , building up layers is key to protecting the paint work.