Typically, when a drummer refers to the number of 'pieces' on a drum set, he is referring to the number of drums only. So, a 7-piece drum set has seven drums regardless of how many cymbals, stands and add-ons are present. So, if a drummer says she has a 30-piece drum set, she has 30 drums and a HUGE practice area!
What you will see on music for drums is a typical music staff. Start at the upper left corner of the staff, just as if you were reading text. The first markings are a clef and a time signature.
A standard drum set is notated using an "X" symbol for cymbals as the note head and a solid note head for the drums.
Each line or space is assigned different instruments of the set. Typically, the very top of the staff is the cymbal, then the spaces of the staff from the top down are tom tom, snare and floor tom; bass drum (or kick drum) is usually written in the bottom space of the staff.
The cymbal notation that sits on top of the staff will have more information. It will say: HH (HI HAT), R.C. (RIDE CYMBAL) or CR. (CRASH CYMBAL). These change throughout the piece as the composer indicates.