Go through your closet and select simple but flattering items. Unless you've been directed otherwise, casual dress is fine for an audition. Opt for something fashionable but not over-the-top trendy--dark jeans with clean lines frequently work well for both men and women.
Choose an outfit that lets you melt into your character but that still shows some of your own personality. A shirt with a subdued but interesting pattern is a nice way to achieve this. Small, tasteful yet intriguing details on your clothes, such as contrast stitching on a well-cut jacket or antique buttons on a simple blouse, can also help you stand out in a way that isn't distracting.
Add a simple prop or costume item to your basic monologue outfit if you truly think it will help your performance. While entering your audition dressed head to toe as an emergency room surgeon might brand you as an amateur, a minimal accessory such as a surgical mask or stethoscope could potentially strengthen your act.
Let the part for which you're auditioning influence your dress in subtle (but hopefully persuasive) ways. If you're going for the part of the beautiful mistress, for instance, wear an outfit that shows off your figure to the best advantage and take some extra time with your make-up and hair. As long as you keep the colors, fabrics and lines of your clothing simple, you can nudge your look in any number of directions.
Practice your monologue in the outfit you plan to wear for your audition. If any part of your ensemble is uncomfortable or seems to attract too much attention to itself, switch it out for something else. Make sure you're thoroughly content with your outfit before the big day--if you feel good in what you're wearing, you'll be more confident.