Not All Steps Are Created Equal
It is important to remember that not all dance steps are created equal. In virtually all styles of dance, the choreography is built of important, striking steps or positions connected by lesser, or preparatory, movements. When faced with a new combination, immediately identify the high points—those important, often big, accented or emphasized movements—and make them your priority. Learn exactly how and, most important, when they should be done. Not only is it disastrous if you do a big kick, turn, or leap a count ahead of or behind everyone else, but getting the big movements on the right counts will also help the rest of the steps fall naturally into place. For example, if you are determined to kick your right leg on the count of four, chances are that your body's innate kinesthetic intelligence will lead you to make the move before it some sort of weight shift onto the left leg on the count of three, even if you hadn't yet memorized the particular step that does that.
Just as it's easier to memorize a sentence than a list of single words, it's easier to remember a phrase of choreography than a string of individual steps. Try to see the audition combination as a collection of just a few phrases that begin, develop, and end with some sort of choreographic logic. Contained within the phrases will be preparations, high points, "connective tissue," and resolutions. If you can find the "sense" in the way the combination is constructed, it becomes easier to remember what follows what, and you won't feel daunted by the idea of having to memorize a series of randomly ordered moves.
When you are first presented with the combination, get your body involved immediately in the learning and memorization process. Don't stand still and watch the demonstrator do the movements over and over. Move your body while you watch! Get the body's powerful muscle-memory system working as soon as you can by physically imitating what you are seeing from the very beginning. It is through repetition that choreography gets embedded into your muscle memory, and the sooner you can get portions of the combination committed to that memory, the faster your learning process will be.
As you try to learn the details of the combination, trust your body's natural inclinations, especially if you've had a lot of dance training. Rather than wasting a lot of time trying to sort out and memorize each and every weight shift, arm action, or plié, you can often rely on your body to figure out those things in response to the overall flow of a phrase. For example, your knees will naturally want to bend when you come down from a jump or before you relevé, and your arms will often place themselves in natural opposition to certain twisting, turning, or spiraling movements. Keep your mind focused on the big picture; think ahead. If you make a mistake, forget it—instantly! Even when you're just learning or practicing the combination, don't focus on what you did wrong. You don't want to give a mistake any additional time to settle into your memory, muscle or otherwise.
Why This Dance?
It is also helpful to grasp why the choreographer is asking you to do this particular combination. If you are not told outright, then try to figure out the general theme of the combination. Is it a story? If so, then focus on clarity of action and character development over all else. Is it about angular shapes, fast footwork, or pirouettes? If a combination contains lots of seemingly unrelated "tricks," then clearly they are testing your technique, and technical execution should be your primary concern. Or maybe the combination is about style or rhythm? In those cases, look for the stylistic idiosyncrasies or unusual syncopations and concentrate first on those aspects of the combination.
During those times when it's inappropriate for you to be moving, imagine yourself doing the movements. This helps your body's nervous system memorize the coordinations. It's the same principle behind why injured athletes engage in "mental practice," imagining themselves pitching, for example. They often rehabilitate much faster if they keep the neurological coordinations "in shape" even while the rest of the body is not able to fully execute the motions.
Lastly, don't underestimate the importance of practice. Taking dance classes that are outside of your usual technique or style is a good way to gain experience in picking up different kinds of combinations quickly. If that becomes too expensive, you can always get together with a few dancer friends and take turns speedily teaching each other challenging movement combinations.