While you may decide to bring in extra-textual information that has a bearing on your argument, such as biographical information, historical background, or psychological parallels, most college literary essays also pay very close attention to the primary work. "To analyze" means to pull something apart to carefully examine the pieces.
When you analyze a poem, a story, a novel, or a play, you select lines or passages to discuss to make a claim about the whole work. Sometimes you interpret the objects the author has written about: Is the red dress seductive? Sometimes you explain the patterns of imagery and metaphors the author has created: Why are so many women compared with food in Aphra Behn's The Rover?
Just as you want to avoid hubristic claims of "proof" in your thesis, you should also avoid shy qualifications.
There is no need to muffle your thoughts with phrases like, "I believe that" or "In my opinion." Your reader assumes that everything you write that you do not attribute to another author is your opinion. Whether your essay is three pages or twenty, you want to use your space to make a case for your thesis.
The essay's conclusion thoughtfully reflects on what you have presented in the paper. Your professor and your fellow students are doubtless aware of Shakespeare's well-received reputation and have no need for information extraneous to your topic.
Only include such phrases if they startlingly contrast commonly received ideas.
Reading a poem like Dylan Thomas' "Do Not Go Gentle into that Good Night" might force you to face your love and grief for a parent or relative who has died.
The cathartic power of art has been appreciated since the days of the early Greeks, and an emotional response to a work of literature is a legitimate response.
Make sure you discuss the poem, not simply the friend John Keats seems to be describing; analyze the force of John Donne's imagery rather than the religious experience you have had. It is as impossible to prescribe a formula for the opening line of a literary essay as it is to tell a poet or novelist what the first line of her literary work should be.
If you believe that your purpose is simply to satisfy an assignment that scarcely interests you, feel free to start your essay with a sentence that will allow your reader to share your boredom.