Note the key signature: The piece is written in the key of C with no sharps or flats.
Note that the time signature is 4/4 or common time. There are four beats per measure and four quarter notes equal one beat.
Note where the song repeats: After the four measure introduction, a new section begins at measure 5 (where the right hand begins the melody). The first ending is marked at measure 10 which returns to measure 5. The second ending (at measure 11) introduces the middle portion and continues until measure 18 which is marked "D.S. al Coda" to take the player back to measure 5. The piece is then played through measure 9 and then concludes with the two-measure Coda in which the piece fades out to the end.
Before you play, try playing some arpeggios to loosen your fingers. This is especially important for your left hand because it will be repeating the same arpeggio pattern for most of the piece. Begin by playing the left hand and right hand separately. Play them together when you feel confident enough.
Play as far as 14 measures, or the main section of the song, which will then repeat. Play slowly and gradually build up speed until you can play at tempo. (Listen to a recording of the "Charlie Brown Christmas" soundtrack and compare its tempo to yours.) Repeat the process until you can play the music with no mistakes or pauses.
Move on to the middle portion of the piece, practicing it until you can play it smoothly. Note: While this portion is only nine measures long, it can be difficult to play it smoothly as it shifts octaves.
When you have both portions, play the entire song from start to finish. Mark any mistakes you make on the sheet music so you can work on them later. Write down the fingering if you need to (many portions call for playing two notes at once on the same hand). Pay special attention to the transition from the main portion to the middle nine measures and back again.