One can analyze John Donne's "Farewell to Love" in a variety of ways. Let me give you some examples of aspects of the poem to analyze. First, you could look at the historical context of the poem. The poem was written in England in the early 17th century.
Second, one could examine the life of the poet. Donne was a devotely religious man who also wrote love poetry with sexually explicit imagery. Much of his work focuses on the tension between the sacred and the profane.
Third, you could analyze the style of the poem. "Farewell to Love" has a traditional rhyme scheme but utilizes lines of varying meter and length.
Fourth, you could focus on the imagery and figurative language. For example, Donne compares lovers to "atheists at their dying hour," which draws connections between love and faith; courting the person we love is much like calling out to a deity we are not sure exists. Donne also refers to "His Highness sitting in a golden chair," which suggests a comparison between devotion to a lover and allegiance to a monarch.
Finally, you can analyze whatever aspects of the poem you find most interesting, confusing, or provocative. For example, you might wonder what "worm seed" is, so you could research it and figure out and why it is mentioned at the end of the poem.