Practice reading through lines of a script you've never scene before. Give yourself 15 minutes to speak the words as you read and develop the tone in which you will say them during a real audition. Practicing cold reads outside of an audition improve your confidence and ability to memorize lines.
Relate what the character is going through to a time in your life from which you share a similar experience, or an experience that would trigger a similar reaction. For example, if the character is sad, think of a time in your life where you suffered a terrible tragedy. This will help you create an emotion to take into the audition. Some actors forget to do this during cold-read auditions, but it will improve the natural delivery of your lines.
Practice saying your lines without looking at the script. Read a couple sentences and then look up to say your lines. This is a better alternative than straight reading because the casting director will be able to see your face and you will be more natural.
Bring your script with you when called into the audition. This could improve how comfortable you are with the lines because you will have a backup plan in case you haven't memorized everything -- complete memorization is rare in cold reads. Look at your lines when the other character speaks. Try to look at the lines as little as possible so that you can react to what the reader is saying.
React to what the other character says and then say your lines. This will make your line delivery more natural. Try as much as possible not to look at the script as you say the lines. If you can't remember your line, look at the script and then back up to deliver your line, rather than reading directly from the script.