Performing Shakespeare is very different from performing most other scripts. Keep in mind that when Shakespeare's texts were written, English was still evolving as a new language. Like other acting and audition skills, performing Shakespeare improves with time, experience, and training. Even if it is your first experience with Shakespeare, there are some things you can do to make it easier.
Shakespeare Acting Tip #1: The Verses
Shakespeare is written in verse. One of the most beginner mistakes is to actually recite the verses, pausing at the end of each line, the way you might read a poem aloud in elementary school. To read Shakespeare well, you have to read beyond the verses to communicate the meaning behind the words, which brings us to our second tip...
Shakespeare Acting Tip #2: The Words
In order to perform Shakespeare well it is absolutely essential that you understand everything that you are saying. And I do mean everything. This can seem like a daunting and nearly impossible task but there are a number of resources that can make this much easier. If you are serious about becoming a professional stage actor, you really must own a good Shakespeare anthology. My own anthology that I use is the Norton Shakespeare, which is well footnoted and defines unfamiliar words, as well as providing a lengthy explanation of the meaning & context of each play. My companion resource is the Essential Shakespeare Handbook, which allows me to look up key information quickly.
Shakespeare Acting Tip #3: Acting Normal
I have seen many very talented actors turn into idiots when they perform Shakespeare. I like to call it the "Shakespeare disease": all of a sudden a perfectly good actor starts clutching his heart, flinging his arms around, and rapidly changing the pitch of his voice like an adolescent boy. Reading Shakespeare is like reading any other play. You should play it as naturally as possible - no overacting or emoting necessary.
Links to More Shakespeare Acting Tips
Playing Shakespeare : An Actor's Guide
Acting Shakespeare
Secrets of Acting Shakespeare; The Original Approach
Clues to Acting Shakespeare: Skills Clarified for the Actor, Student, and Reader
Shakespeare without Fear : A User-Friendly Guide to Acting Shakespeare

Vintage Stratford Map Script Tote