How to learn scripts quickly
Everyone will have a way of memorizing lines that works best for them, so the following are just a few suggestions which you can try in order to find out what works best for you.
Learning lines can be particularly intimidating when you have huge monologues to say, as is common in Shakespeare. In such a situation, the best thing to do is break an extended passage down into small chunks. Don't worry about learning it all at once; memorize about four or five lines, then go away and do something else before returning to the script and seeing if you have memorized it correctly. You may feel that this takes more time, but it is better than trying to learn it all at once and then finding you have forgotten the earliest lines.
For some performers, the best way of learning a script is to just read the script and say the lines out loud over and over again; you would be surprised at how much you remember from just doing this. I believe the most effective time to do this is just before going to bed, as you actually retain the information much better. As well as looking at your own lines, though, it is imperative to keep track of your cues, else you will know what your lines are but not when you should say them. To help you with this, try to find someone who can read the other performers' lines for you, as that will help you to build up a general idea of what they are saying and what you need to listen out for before you speak. The best person to read the script with you would be the actor who is actually performing with you, as they should be the most willing to go through each scene again and again, in small sections if necessary, in order to help them learn their lines as well. Of course, it is not always possible to meet up with your fellow actors outside of rehearsals, but you could always try asking them to go to one side with you during a rehearsal if there is a time when you are not needed in order to go through your words quietly.
For a more auditory approach, try recording your lines and then listening to them repeatedly, particularly when you are on the move, for example walking, shopping or doing the house work. This means that you make the most of every spare minute you have, which is crucial when you have limited time to learn your lines.
If you are in a play which is commonly performed or of which there is a film version, it may be a good idea to watch/ listen to your scenes on YouTube and/or buy the DVD version, as this is a more relaxed way to learn lines in comparison with sitting down with the script and desperately trying to memorize the words line by line. However, if you do pursue this technique, pay attention to differences in the scripts there will inevitably be between versions.
Some people have a more visual mind, so it helps them to look at a script over and over again until they can picture the words in their mind. This approach would suit someone with a photographic memory. Also, you could try hand-writing your lines as you would if you were trying to remember something for an exam.
There are so many techniques that work for learning scripts quickly, so the best thing to do is to try a selection of the aforementioned ones in order to see have effective each one is for you.