If you want to look like you belong in Blue Man Group, you need a blue face. Get a bald cap and blue body paint from a costume store. Cover your hair with the cap and cover your face with the blue paint. Feel free to shave your head instead of using a bald cap.
The basic Blue Man costume is all-black. Any long-sleeve T-shirt and black pants will do. Don't use a shirt that is too valuable, because you don't want any blue paint stains on it. You will also want black shoes. Wear blue gloves. If you want to be physically energetic and really get into the role, wear loose and comfortable clothes that let you move around freely.
The Blue Man Group's best-known act is banging on constructions of PVC pipe to make music. Whether or not you are a musician, you will need a piece of PVC pipe and a drumstick. You don't need to be able to play it. Just whack on the pipe with the drumstick from time to time, and when you are showing people your costume for the first time. It will create a humorous sort of realism.
Music is at the heart of the Blue Man show, so you will need music to complete your costume. Buy a Blue Man Group CD and bring a boom box along. Put the CD in the boom box and pantomime your own version of the Blue Man spectacle. You might not impress anyone with your talent, but they will at least appreciate your sense of humor.