Break down the kit at least into the separate shells, hardware, and cymbal. Arrange the components from largest to smallest.
Spray the cleaning agent on a rag and begin with a standard metallic cymbal stand. Wipe the metal down until it is shiny and reflective. Almost any light household cleaner will be acceptable to use on metal.
Go to your local specialty drum store, which will sell cleaning material meant to shine the cymbals without leaving streaks or residue. If you know the kind of material your cymbal is made from, get any cleaner that works on the material. Press lightly and rub along the grooves in the top of the metal to clean your cymbal.
Find out what kind of finish you have on your drum shells; it is imperative to picking the right cleaning supplies for your shells. With lacquer, do not use hot water, as it will loosen the finish. Ensure that your cleaning product won't strip or discolor your drum shells by reading the back of the cleaning product carefully. Once you know you have a safe cleaning material, wipe gently around the shell in long strokes or in large circular patterns.
Reconstruct your kit now that your shells, cymbals and stands are shiny and clean. If you are cleaning in preparation for a show, remember to tune your kit before performing.