Step 1: Learning Your Character/Life Experience
Sometimes it really helps to try your best to get in your characters shoes, that way you're not so much faking the emotional responses of them, more acting them out which is different. one way that can make it easier is to draw on your own experiences in life, at least for basic emotional responses and for more complicated stuff, remember it mightn't be an exact replica of what happened to the character but it can work, more so if the end feelings you had and what the character is to have are in line with each other.
Take the time to read the whole script, learn how your character is taken in by others, look at them objectively, not as if you are them as well as your version of them, it's important to do so because then you have some idea of what you believe the character is like.
Some times surrounding literature can be a big help here, as well as asking the directors etc. how they want to see the character be realized, it's open to interpretation but it's their call how to interpret it.
Step 2: Memorizing Lines...
Everyone has their own way of learning their lines and whatever works for you is fine, as long as it's not writing it on your hands...
So the problem isn't learning them, it tends to be recalling them, you're going to have to chill out and calm down, don't get ahead of yourself and don't panic when that one line comes, up, sometimes what you were in your head will jar your memory in to action again since it makes it linear if you remember your lines by reading them all through like one block. If that doesn't work try thinking of the reply to the line just said, it's easy if you know what they just said much of the time because you have a rough idea of what anyone would say to help bring that line up from the murky depths of that mud pit you call a mind. Anyway once you're on stage you need to be in your element, having a lot of rehearsals in front of all the crew can really help, once you're up there and get on form it's much easier to keep chilled out. Now the key to recalling a line is not to freeze and panic, when you do that it makes it ten times harder to remember the line.
Step 3: Know Your Part
Step 4: Listen Carefully.
Don't just remember what the people said, take it on and adjust accordingly, if you forget to put sugar in your coffee you'll go spoon it in won't you?
Step 5: On Stage.
Another important thing is to project your voice. You need everyone in the audience to hear you. Don't be afraid. Speak loud and clear and with emotion. Don't use monotone.