The Drum kit usually consists of 5 drums and 3 cymbals. Smaller 18" bass drums are sometimes used in small Bebop Jazz drum sets. In Rock bass drums are usually 20" or 22". Snare Drums are usually 14" and can be made of either wood or metal. Toms range in sizes from 8"-18". Having only 1 mounted tom and one floor tom was common until the 70's. Three toms is usual now. Drum kits usually consist of a pair of 14" Hi-Hats, a 16' Crash cymbal, and a 20" Ride cymbal. Some drummers have many more cymbals to expand there sound pallet.
Drums are usually written as notes, and cymbals are usually notated with X's
The Big drums are written down low in the stave and go higher as the drums get smaller.