Listen to a recording of "Smoke on the Water" to get a feel for the rhythm and mood of the song. Notice how the feel of the song is somewhat dark and brooding, and try to replicate this mood when you play the melody on the piano. Concentrate on the bass line -- this is what you'll be playing first on the piano.
Decide what key you'd like to play the song in. "Smoke on the Water" will work in a variety of keys, but most people think it sounds best in the key of D. If you're playing the piano to accompany a guitar player or vocalist on this song, talk to them and see if they're more comfortable playing it in an alternate key.
Learn the notes used in "Smoke on the Water." In the key of D, the notes will include D, F, G, and G sharp, typically represented by G#. In order, the notes you play will be as follows: D, F, G -- D, F, G#, G -- D, F, G -- F, G. Be sure to play the notes using the correct rhythm as heard in the song. If you get confused, try playing along with a metronome.
Notice the relationship of the notes on the keyboard. This will allow you to play the song in different keys. Only four notes are included in the song. The second note is three keys above the first, the third note is two keys above the second, and the fourth note is one key above the third. Using this rule, we can transpose the melody to a different key, such as C. In the key of C, the notes would then be C, D#, F, and F#.
Play along with a recording of the song to be sure that you time each note correctly. In addition, practicing in this manner will hone your ability to keep time over the course of a song. This is a useful skill to possess regardless of what song or instrument you happen to play.