Learning lines freaks most drama students out to an incredible extent. I find this sad, because it's really not difficult. It may be time consuming, but if that's your concern, I'm afraid you are disgustingly lazy. I'd like to say up front that I am aware that there are many different methods of memorizing text; this is just my method, and in my experience it works like a charm. However if any of you know of other ways, let me know in the comments! Lets do this in steps.
What you wanna do first, is separate your script into sections. The script as a whole is first divided into acts, acts into scenes and scenes into thoughts. It is important for us to follow this guideline in breaking out scripts into manageable chunks, so that the whole task of learning lines becomes less daunting. Most scripts are already divided for us as far as the third step (scenes), but it is up to us to divide them further into thoughts. We do this by identifying the ideas and steps within the scene, separating them and, only for a little while, isolating them. Each new 'idea' can be indicated with a square bracket, as shown below.
The next step is to highlight sets of lines with different colours, so that attention can be given to each set individually, as I've done to the monologue below. I've blurred the words out so I don't get slammed with copyright lawsuits. The idea is that we highlight lines in sets of two's (a line here meaning sentence). I've given an example below.
The third and final step is where the actual work comes in. This is the part where you start to learn your lines. Scared? Don't be. I'm about to give you a really simple method that will make all the difference to the amount of time you spend studying your text. What you do is, learn the first set of lines you've highlighted, so that you know them 100% off by heart. For the average person, learning two lines takes approximately five minutes. One you've remembered the first two lines, move onto learn the next two. When you've remembered those, try to recite all four lines. When you can do this, move onto the third set of two. Then try to recite all six that you've learnt. Continue this cycle until you've reached the end of the section. Then, restart the process with the next section. Once you've memorized the next section, try to recite the two sections you've learnt. Make sure that you speak the lines you are trying to learn out loud. That is the only way this works!
Once you've memorized the entire script using this method, it is imperative that you practice reciting your lines everyday! This is the only thing that will solidify them in your mind. Remember to say them out loud!
"Thats all very well," I hear you say, "but what about dialogs?!" No problem! What you do, is speak your lines out loud, and read the other person's lines in silence. This seems to create a divide in one's mind between the lines one must say and the lines one must be 'fed' by the other actor(s).
There you have it! Try it out and let me know how well it works for you!