Removing rust on a cars body work can be a very time consuming and expensive task, it all depends on the severity of rust. Most cars that show signs of rust that are within 3-5 years of manufacture can have the rust removed quite successfully, for the rust on the effected panel hasn't had sufficient enough time to eat in to the metal to cause extensive damage and warrant a large repair. Most car manufactures offer a 5 year paint warranty that covers you for rust, but beware that if the rust has been caused by a stone chip, panel scratch or scrape and not some defect or abnormality in the cars manufacture then you might not be able to use your paint work warranty protection.
If the rust is quite light and small and has not had the chance to bubble up then you can either have the rust removed at a body shop or you can use a Smart Repair or Mobile Car Body Repair specialist. The smart repairer or mobile car body repair specialist is the cheaper option to the body shop or accident repair centre; they would be able to come to your home or place of work to carry out the rust repair and should be able to remove the rust quite successfully. The finish from a body shop repair is just as good but they would take your vehicle away for a number of days in order to repair the rust.
If the rust has had time to fester and starts to bubble up and blister the options for Rust Repair start to get slim. You can cut out the rust and weald another section back on or you can re-skin the effected panel (reskinning a panel involves removing the outer skin of a panel and re-welding a new one back on) another options would be to remove the panel entirely and to replace it with a new one. Replacing a panel is the preferred choice for body shops and accident repair centres for there is no chance of the rust repapering after the new panel has been fitted.
The best way to prevent the build up of rust on your vehicle in the first place is to be vigilant and check vulnerable points on the car like the wheel arches and seals, making sure there is no build up of water at least once a week.