Read through the text to identify any unfamiliar words or phrases. Refer to the footnotes of each page for translation of unknown words and information regarding the histories of phrases and the contexts in which Shakespeare used these words and phrases.
Read the text aloud so you can hear the sound and rhythm of the language. "How to Read Shakespeare's Sonnets" (see References) advises that much of the meaning we extract from a line depends on the way in which we read it. According to the article, reading just one word in the wrong tone can change the meaning of a sentence (or paragraph) entirely.
Remember that dialogue within a play is conversation, and read it as such. Pause at periods and commas. Try reading with a partner and acting out scenes as though the two of you are having a normal conversation. This will make the language sound more natural and less intimidating.
Connect themes that are common to everyday life or that reoccur in various forms of literature. Start with what you know about love, anger, tragedy, etc. and connect that knowledge to Shakespeare's works. Themes reappear over time; all that really changes is context. If it helps, think of the story in a modern context to which you can relate more easily.
Consult the Internet for countless scholarly articles about the Shakespearean text you are reading. Entire courses are dedicated to the study of Shakespeare, and many students and professors publish their studies and analyses online.
Consult one of the many available books devoted to criticism of Shakespeare. You're sure to find one devoted to your particular interest in Shakespeare studies. Try "Shakespeare's Words: A Glossary and Language Companion" by David Crystal and Ben Crystal, which dissects problems words through a process known as lexical triangulation. "The Oxford Companion to Shakespeare" by Stanley Wells contains more than 3,000 entries on various Shakespeare-related topics, approaching each with Oxford's esteemed "rigor and authority," according to the Library Journal.