Whether you're getting ready to audition, or you've booked the job - a film, play, commercial, webseries, etc. - and have a bunch of lines to memorize, you can experience anxiety over not having your lines totally memorized.
So, let's look at a few things we can do to get comfortable with our dialogue.
First and most important - know what you're saying and why! This may seem like a no-brainer, but you might be surprised at how many actors go into an audition without being clear about what their lines mean. Sometimes this happens because you are getting out-of-context "sides" a fairly short time before going in to audition. And you can't really have a long discussion with the casting director about what the lines mean. When a CD asks if you have any questions, they mean do you have ONE question that you really couldn't figure out on your own. And that's the key to knowing what you are saying - if it isn't clear, make something up! You can't spend three days memorizing your lines without having any idea of what you're saying and then go into the audition room and find out then. Most of the time the CD wants to see what you bring to the role - what you came up with. Then, if it's not on track, they'll give you an adjustment.
Anyway, back to those tips for memorizing lines. Never spend all your time sitting in a chair or standing in front of a mirror, or in any one position. Why? Because the minute you start to move around and/or handle props it will throw you off. When you're at home, after you have the lines a little bit down, start to do stuff while you say the lines: wash dishes, make the bed, check your Twitter feed, whatever - just do stuff.
Do research if there is a word or phrase that you are unfamiliar with. If you don't, you can be sure that you will stumble over that word in the audition (or performance).
Picture your environment - set the location in your mind - where this scene takes place. See the stuff around you and pretend you are interacting with it.
When rehearsing, speak the lines with all kinds of different emotions. Even if you are supposed to be sad in the scene, try it once laughing and once angry. Not only will this help you to get the lines firmly in your brain, but you may also find that there is something you can use from those other readings!
Speak the lines in gibberish - this will help set the emotional tone of the dialogue without words.
In fact, if there is a word that is difficult to say, try saying it a few times in gibberish, then say the word the correct way. At least for me, I find this often helps.
Run your dialogue once or twice just before going to sleep. And then first thing when you wake up.
And last, take breaks. Don't run your lines all day every day. Not only will this not help, but the dialogue will begin to feel stale and your emotions fake. Leave room for some spontaneity, even if it means you might blow a word or two. No one is interested in hearing the dialogue perfectly said by a machine.
This are the tips I use myself that I have learned over the years - hope they help.
And here's a shameless plug for my ebook with contains more of this kind of advice:
An Actor's Guide to Auditioning