Did People Really Speak The Way They Do In Shakespeare's Plays?

One also has to consider the fact, that  Shakespeare was writing in his 'natural ' accent, South Warwickshire argot. Therefore, in Henry V for instance, he has the Duke of Burgundy, one of the most influential and powerful men in the whole of France, talking about 'Burrs and Keksies!' 

    These are small buds and weeds that adhere to the clothes when walking through a field in Summer.

    However, I doubt sincerely that John, le Duc de Burgundy, ever knew what a burr or a keksie were!

  It is well also, to consider Henry V from the layman's point of view. Many in the original audience were uneducated to the point of illiteracy, therefore understanding Shakespeare, was a bit of a trial!  When he was writing about the Eastcheap gang, (Pistol, Bardolph, Falstaff etc), he naturally fell into his natural Warwickshire argot, so Mistress Quickly, when describing the death of Falstaff, uses 'a' when meaning he, she, it, of, and 'and' etc!

  "A' babbled a' green fields", can be 'interpreted' as, "HE babbled OF green fields"  Suggesting falstaff was reciting the 23rd psalm as he lay dying, "The Lord is my shepherd I shall not want, he maketh me to lie down in green pastures".

Yes, back then they spoke the same way they do in shakespeare's writings.

An interesting 'sideline', to this question, is the number of everyday phrases we use, 'invented', during Shakespeare's writings.
I do not say he actually invented them, but scholars and historians constantly point to them, for instance:
"A foregone conclusion"
"A tower of strength"
"Bated breath"
"Dead as a doornail"
"I have not slept a wink"
"Wild goose chase", and countless others.
Also. You have to look at the words he 'invented',
"Advertising, drug, fashionable, grovel, investment, numb, premeditated". All used in the general wordplay of the work he was writing at the time, and all incorporated so technically into the work that a general audience immediately understood the meaning of the word.

No they didnt