Deputy headmistress at the Hogwarts School of Witchcraft and Wizardry, stern Professor Minerva McGonagall is one of the kind and trustworthy adults in Harry Potter's world. To dress as the good professor, start with the all-important hair and glasses.
Put your hair in a tight bun if it happens to be long and black. Consider a temporary color or a wig if your hair isn't long enough or dark enough.
Find a pair of square-framed glasses for McGonagall's trademark specs. Remember that when this professor of transfiguration transforms herself into a tabby cat, the cat has square markings on her face, just like the glasses.
Don an emerald green robe. Professor McGonagall is almost always seen in this color - that is, unless you want to portray the professor when she interrupted a Gryffindor victory party and insisted the students all go to bed. Wear a tartan dressing gown and a hairnet, in that case.
Carry a wand, which no self-respecting wizard or witch would be without.
Emphasize Professor McGonagall's love of Quidditch, the wizards' favorite sport, by carrying a book on the subject, such as "Quidditch Through the Ages" - which can be found in the Hogwarts library. (As a muggle - a nonmagical person - you might have to just make a cover and put it over another book from your own personal library.)
Carry a lace handkerchief - an accessory Professor McGonagall is carrying when we meet her in the first book, "Harry Potter and the Sorcerer's Stone."
By now, the publicity machine for the film version of "Harry Potter" has firmly implanted Maggie Smith as Professor McGonagall in all our brains. It is a safer bet to go with the films' version of the character, instead of the books', if you want to get instantly recognised.