This is a very interesting question that directors staging A Midsummer Night's Dream by William Shakespeare must think through carefully as they work with designers on a production. The simplest answer to the question is to say that in all the thousands of productions of the play, including stage plays and opera, ballet and film adaptations, and illustrations thereof, spanning the past four centuries, many different actors have portrayed the fairies wearing a wide range of different costumes. Because the earliest texts we have of Shakespeare's plays do not include detailed descriptions of the fairies, we do not know precisely what he had in mind. What we do know for certain is that all of the fairies, including Titania, would have been played by men, as men played all the roles, both male and female, in Elizabethan theater.
Fairies as they were portrayed in Elizabethan art were quite different from the popular images we find in Disney and other modern iconography. Fairies were human sized, did not have wings, and were somewhat darker by nature. Fairies (as Titania and Oberon) were prone to stealing human children and people left out bribes such as milk to propitiate fairies. Pictures of Puck (also called Robin Goodfellow) from the period show a satyr-like figure resembling the Greek god Pan.
I will just say that the fairies in this play look however the artistic director wants them to look. We make assumptions about the look of fairies based on our cultural exposure to stories and images of them. We expect that whoever performs the fairy roles will be agile, graceful and light in terms of energy. There are different kinds of fairies in the play and their physicality should reflect that. There are the the King and Queen, who have all the characteristics of the fairies plus a strong, regal presence, clearly distinguishing them from the other fairies who do their bidding. Then there is Puck, who is not exactly a fairy, who is more earthy in appearance and character than the more wispy fairies who serve Titania, their queen. It is the job of the actors who play these roles to appear to be denizens of an alternate reality, coinciding with our own, but more ephemeral and way less solid.