If the paint is just oxidized and not beat up, per say, then I would try a clay bar. Paint clay bar kits can be bought at any car parts store in the detailing section. Meguiar's and Mother's make a nice kit available there for about $30. The kit comes with a bottle of detailing spray, spray the surface and use the clay in a small circular motion with light pressure. Keep massaging the paint with the clay until you feel it move smoothly over the surface, then move onto the next spot. Keep folding the clay over frequently to keep the cleaned dirt particles trapped deep in the clay itself. Keep in mind, this will remove any wax, so the paint will need a good coat or 2 of wax.