This is the Peacham Manuscript. It is the only surviving manuscript from the time of Shakespeare and the only surviving documentation of the costumes that actors might have worn on stage. The image is of a performance of Titus Andronicus.
Take a closer look at the image and the central character, is wearing a toga and laurel wreath, suggesting that she is from ancient Rome. The remaining characters, however, appear in Elizabethan dress – soldier’s outfits and the like from the time. It would be rightly said that as a director, Shakespeare chose to use modern dress from his time for costume.
Whether this is a truly reliable statement can’t be verified, but it was the case that the majority of the costumes Shakespeare used was contemporary. It was whatever the company had to hand that could show to the audience the basic character. Shakespeare wrote in the dialogue where the characters were from and who they were, and he knew that his audience of the time were used to listening out for those clues, so he asked his audience, as he did with the set, to imagine that the costumes his actors were representations of what the actors should have been wearing.
The company would have had a costume store which they would have returned to again and again, adapting here and there and adding trinkets like brooches or simple jewellery. The same sorts of characters would have worn the same outfit in different plays – Hero in Much Ado About Nothing might have worn the same dress as Juliet in Romeo and Juliet. This sharing of costumes between shows would also help the audience to identify the stock characters, the villain, the love interest, the male protagonist etc… The costumes also helped the audience identify the status of the character. Elizabethan life at the time was very concerned about status and a lot of emphasis was placed on dressing to show your status in society. The actors at the time would have done the same, taking costumes that reflected the social class of the character.
With regards to costume, set and props, Shakespeare was a pioneer of, what we think of as a modern term, suspending disbelief and asked his audience to see something that wasn’t actually there.