Debbi, if you really have brass fixtures, first you have to strip of any clear coating. You can use something like Citristrip for this. Next, get a polishing wheel for your electric drill and some jeweler's rouge. Hold the rouge on the wheel to transfer a little to the cotton wheel then hold the wheel on the brass. Keep the wheel from staying in one place for long and add more rouge every so often. This will quickly remove the tarnish. You might also use a small wheel on a Dremel tool to get in the tight places. When you have all the tarnish removed and the piece sort of shiny, wash the residue off with mineral spirits on a rag and then spray on a coat of clear lacquer.
You can easily tell if a piece is real brass or brass plated by putting a magnet. The magnet will not stick to real brass but it will stick to steel that has been brass plated. Sometimes fixtures are plated pot metal, so you next want to scratch an out of the way spot. If the bottom of the scratch is grey metallic looking, it is pot metal. If the bottom stays the yellow brass color, it is real brass.