You should always arrive at an audition for a musical production with a prepared song. Find out from the director or auditioners in advance whether they prefer you sing something from "Grease" or another musical. You should prepare both an "up-tempo" song and a ballad. This way you'll show how well you can carry a fast-paced tune as well as a more lyrical number. For guys choosing a song from "Grease," try "Beauty School Dropout." Girls should consider "Look at Me, I'm Sandra Dee." If you're auditioning for the leads and want to consider songs from other musicals, those audtioning for Sandy should look at anything sung by Laurey from "Oklahoma," while those auditioning for Danny could have fun with an Elvis tune.
You probably won't be asked to present a prepared monologue for a "Grease" audition, but you will be asked read from the script. You could also watch a recording of the Broadway show or the movie version to get some tips on the characters. Make sure that you know the story and the characters when you show up to audition. When you are given a scene to read and a scene partner to read with, make sure that you take some time to read through the scene before you present it to the auditioners. Make bold choices that demonstrate the character (for example, pretend to chew a big wad of gum, if you're reading for Rizzo) and speak clearly and with a strong, generous vocal quality.
Prepare for the dance combination that you'll be taught at auditions by previewing the dance numbers from the movie or Broadway versions of "Grease." You might also practice some traditional couples' dances from the 1950s, in preparation for the audition. Wear an outfit to auditions that allows you to move freely, and bring along some character shoes or jazz shoes to wear for the dance portion of the audition. You will probably learn a dance combination from the show's choreographer and then present it in a group to the auditioners. Try to find a place on the front row when you dance for the auditioners, so that you can show off your dance skills without being hidden in the back.
If you are invited to callbacks (the next audition after an open call), pay close attention to what you are asked to do to prepare. Often, you will be called back to read and sing for one particular character, so prepare a song that character sings in "Grease" and arrive at callbacks dressed in a way that is similar to the way you see this character's costuming. For example, choose a sweater set and knee-length full, loose skirt for Sandy or a leather jacket and jeans for Danny. Consider character touches (for example "tough guy" gestures for Danny and a more shy and innocent demeanor for Sandy) that you can add to any scene reading you are asked to do.