So many new actors get intimidated by the process of memorizing, but the truth is that it is actually one of the easiest parts of the job, Rote memorization is the key...
The crazy thing about rote memorization techniques is how effective they are in such a short period of time. In one hour, one of my students memorized one of the longest monologues from A STREETCAR NAMED DESIRE. In 30 minutes, another memorized a 6 page scene from THE DEPARTED. It happens fast.
Spend some time repeating your cues and lines in a monotone. You don't want to lock in performance choices while memorizing, so I can't stress the monotone enough. Repeat the line five times, put the sides down, and repeat again. Then move onto the next. Once that's memorized, go back to the top of the scene. Just keep working at it, one line at a time. Although the process is tedious and repetitive, you'll be astonished how fast your lines become second nature. And if you're struggling a bit, keep chipping away! You'll likely wake up the next morning completely off-book and, best of all, you won't even have to work that hard to do it!
Once you are completely memorized, the fun begins: When you don't have to think about checking your sides or cues, you get to really play and start focusing on the performance.