Since your question is a bit cryptic, I will play devil's advocate infused with a bit of dry humor and guess that when you say "were" you are implying "during Shakespeare's time." In that case, one of the most important characteristics of a Shakespearean actor is that he was, in fact, a man. If you have any doubt about the veracity of this (and I hate to use such a contemporary movie as evidence, but ...), be sure to watch Shakespeare in Love. At least the humorous spin should give any lover of Shakespeare a good laugh, ... (perhaps as the "real" Shakespeare, whomever he may be, rolls over in his grave).
I am going to assume that by Shakespearean actor, you mean a contemporary and classically trained actor.
Most serious actors understand that all good acting lies in the challenges given by the classics, Shakespeare in particular. A classically trained actor can do anything from classic to modern but an actor who has not studied classical acting will not be able to meet the challenge of Shakespeare or any of the classical playwrights.
Not only does an actor study how to use his body through dance and classes in stage combat, he also works on his voice. Knowing and understanding vocal production is important.
Perhaps the most important courses for a classically trained actor are classes in language. By being able to break down language and understand how it is used to give actors important information about their character, mood, tone, action, etc. is extremely important. Shakespeare gave all his character information though the language he gave them. Stage directions and character descriptions were unheard of in the classics for the most part. All vital information is contained in the language.
There is no such thing as a Shakespearean style. What there is, is an understanding of language which good actors use not only in classical work but also in modern. Words are food to actors and Shakespearean actors enjoy the banquet.