Look through the music, identifying what parts may be easy for you and which parts might be difficult.
Learn to play the music. Start by working on one phrase at a time. Try practicing one hand at a time, then playing both hands together.
Repeat the phrase until you are comfortable playing it with the music in front of you.
After becoming comfortable playing one phrase, add on another phrase and play through them until the transitions are smooth. Do this until a significant section of music is playable. For example: from one music cue to the next; an entire period, typically a set of two to four phrases.
Play through the entire section you've just learned to ensure you can play it without rhythmic or tonal mistakes. The goal here is not to be able to play it perfectly, but to be able to play the rhythms and notes correctly with some semblance of dynamics. Perfecting will come with practice.
Turn your music around or set it off to the side and play through the section again, this time without the music. Observe your mistakes and which parts were difficult to play without being able to read along.
Refer to your music. Look at the difficult parts and review them. Repeat Steps 6 and 7 until playing the through the section without music becomes easier.
Work on additional sections of the music by repeating Steps 2 through 7. Be sure to stitch together each new section with the section you've memorized previously, until the entire piece is memorized.