Hi, Amy. Almost all the "brass" door knobs are not brass. They are brass plated steel. The brass plating on these is so thin that it is almost impossible to remove the clear finish and polish the brass without going through the brass to the steel. If your knobs are in this category, you are usually just as well off to replace the whole set of hardware. This is really not that expensive as some of the internal parts are prone to wear and about 10 or 15 years worth of service is about all you are going to get without problems.
If you really do have solid brass hardware which is very expensive, post back and we can tell you how to strip and polish it.