There are a few basic facts about language that will help in reading Shakespeare's language. Number one: any living, spoken language changes over the course of time. Two fundamental ways in which language changes are phonologically (they way words are pronounced) and semantically (what words mean). We can see how some words have changed in their pronunciation by looking at some of Shakespeare's rhymes: food/good and mood/ blood. We can look at differences in American dialects to see how words are pronounced differently by various speech communities. For example, for some people the "s" in "greasy" has a soft "c" sound, but for others the "s" is a voiced "z." However, it is in Shakespeare's use of words that no longer have the same meaning that causes the real trouble. For example, in Act III of "Hamlet" when Ophelia tells Hamlet, "You are naught, you are naught," she means more than what one would say to a misbehaving child. The word "naught" or "naughty" in Shakespeare's day meant "wicked." Ophelia's response to Hamlet's sexual innuendo now makes sense. Again, we can look to our own times for examples of words that have changed their meanings. For example, the word "bad" has lost its original negative meaning (in some contexts) to mean something quite the opposite.
Sometimes words simply disappear. Shakespeare's language made frequent use of "thou," "thee," and "ye." These three words were all forms of the one word we use today: you. Why did Shakespeare use these words and what happened to them? "Thou" was the nominative case pronoun, meaning that it was used as the subject of a sentence, as in "Thou wretched, rash, intruding fool, farewell!" The pronoun "thee" was the objective case form used as the object of verbs and prepositions, as in "Get thee to a nunnery," or "I'll give thee this plague ... ." The pronoun "ye" was simply the plural form of "you." These three pronouns eventually were all replaced by the pronoun "you." They simply went away. We still see attempts by some dialects of American English to preserve a distinction between the plural "ye" and singular "you." Many speakers of American English use words and constructions such as you-all, y'all, youse, youse guys, and you-uns to denote the plural "you."
Apart from changes in pronunciation, meaning, and the loss of some words entirely, Shakespeare's language is denoted by his use of inverted syntax, or, simply, they way he puts his sentences together. The normal word order in a modern English sentence is subject - verb - complement. Shakespeare frequently inverts that order for stylistic reasons, including maintaining meter, creating rhyme, or creating interest by varying his structure. For example, Horatio responds to Marcellus' demand for information with "That can I." A modern reader should have no trouble quickly converting Horatio's response to "I can" without missing a beat of the original. Inverting syntax is a common feature of good writing in our own times, creating interest, variety, and emphasis when needed.
Although it may be tedious to frequently look down at the bottom of the page, most editions of Shakespeare's plays feature myriad footnotes to help decode reading Shakespeare's language. With a little practice, one can soon enjoy his words as they were meant to be understood by his 16th or early 17th century audience.