In addition to the previous answers, Shakespeare's language is what we call 'Early Modern English'. The English Language has gone through many centuries of evolution and it is common to call Shakespeare's language, 'Old English', when in fact this is not true. Old English was the language spoken by the Anglo Saxon conquerors of the British Isles and it is close to Old Icelandic. This was the language in which Beowulf was written. It is very foreign to modern English and quite unrecognisable.
Norman conquest of England in 1066 began what we call 'Middle English'. This was the language of Chaucer and is much more familiar to us today than Old English - though still quite different.
Then we come to the English Renaissance and a linguistic change known as The Great Vowel Shift that completed around the mid 16th century. After this and into the late 16th to the 17th centuries, we have writers such as Donne and Milton, and later Shakespeare and Marlowe writing in Early Modern English.
The changes that shaped the English Language following the Industrial Revolution marks the point where we see genuine modern English that is quite familiar to us today. Jane Austen, Charles Dickens, George Elliot etc.
So Shakespeare's 'Era' is a complicated topic! Since Shakespeare is a literary figure, it would be relevant to consider his 'era' from a linguistic perspective too.
I hope that helps!