As with most other things, memorization is accomplished through repetition.
Many people are always looking for "short-cuts" nowadays. There aren't any short-cuts, so I think if you approach it as a task that can be done, but one that will take time and effort, you will be successful. We always memorized our music in marching band, because it is very difficult to march and focus on reading music at the same time. The playing must become automatic. The memorization slowly occurred as the music was played over and over.
You can do what is called "chunking", which is to learn larger amounts of information in smaller sections, and then put the parts together into the whole. Some suggestions above refer to that concept.
Much memorization occurs through visual memory, which refers to the ability to "see" in the "mind's eye" (visual memory) the material/information on the paper. Work on looking at the songs on the paper, put the paper away, and then try to see it mentally. Kind of like being able to see someone's face in your mind when they are not standing right in front of you.
Bottom line...regular and constant repetition.