Learning lines for a play can be a daunting task, but you're in luck! There are a few tricks you can use to really get the hang of remembering your part for the play.
Since you're working with just one scene of a play, it should be a little easier to memorize than if you were learning a part for an entire play. Writing is an excellent way to help us remember material, so I recommend hand-writing the scene a few times on paper. Additionally, sleep boots our memory retention, so you might find it helpful to hand-write your scene before going to bed. Alternately, have a nap after your writing. Try writing out the whole scene to get a feel for the flow of the scene, then you may wish to hand-copy only your lines.
After a few days or so of reading and writing your scene as practice, you could give your part a test-run by having a friend help you with your lines. Begin by working with the script- your friend(s) read the parts of other characters, and you read your own lines. When you feel up to it, try to go without the script and recite the lines from memory. If you're really struggling with some lines in particular, try this next trick.
Return to hand-writing your lines, but this time try writing down the lines you struggle with in a different color than the rest of the material. Our brains favor written material that is novel in some way- this is called the Von Restorff effect. Use it to your advantage!
If your scene is featured in films or has been recorded previously, you might wish to practice by watching the recorded program. Try to recite the lines in-time with the character(s) on screen.
Most importantly, try not to over-work yourself. Begin preparing for your scene as early as possible so that you have lots of time to memorize the material. Don't work for too long, either- try to take a break every 45 minutes or so to give both your mind and body a chance to rest. If you try to do too much in too little time, you are likely to become stressed and have a difficult time memorizing your material.
Best of luck to you!