Do people talk the way they do in Shakespeare's plays?

No. Most of Shakespeare's plays are written in what is known as blank verse. Blank verse is an unrhymed line of speech written in iambic pentameter. Iambic pentameter is a line of poetry or verse that contains ten syllables (two syllables equal one foot; you may hear this expressed as five feet in future study). The first syllable in a line of iambic pentameter will be unstressed and the second will be stressed and continue in this pattern until the tenth syllable.

o ROmeo, ROmeo! WHEREfore ART thou ROmeo?

Note the lines will often have either nine, ten or eleven syllables but will still follow blank verse.

For the most part, in real life, we speak in various patterns. Occasionally, that will include a blank verse line, but in general, people do not speak this way. Shakespeare's language employed a great deal of puns (word play hinting at two or more meanings to any given word or phrase). Yes, we do speak in puns in day-to-day language, especially when speaking casually or employing common slang with peers. However, Shakespeare’s use of puns was deliberate and measured, and therefore it is likely that we are not quite as deliberate as Shakespeare was when selecting specific speech for his characters. Therefore, though we may find examples of human speech that mirror Shakespeare’s language, we do not, on the whole, speak as Romeo, Juliet, Macbeth, or Lear do.