Alexander Pope is one of the few 18th century poets who's still widely read today, and An Essay on Man is one of his most popular works. It's quite likely to come up as an essay topic, and if you have to write an analysis of it your first question will probably be where to start. That really depends on what your exact task is; if you have to look at one aspect of the poem - its imagery, for example - your research will be quite different to that for a general analysis. Here are some ideas for an analysis essay on this poem.
The poem is extremely long and is broken into four epistles - letters - each of which is intended to explore a different aspect of human nature. Within each epistle the structure is simple; it is written in couplets, where every group of two lines rhyme and have the same meter. Rhyme and meter frequently change quite a lot between successive line pairs, however.
The overarching theme of the poem is human nature, but this is broken down into many smaller themes. In fact each epistle is prefaced by a summary, around 300 words log, of the themes it covers. It is quite impossible to examine each theme individually without writing a fairly long book; for an essay it's best to stick with the group of themes represented by each epistle. These are as follows:
With each epistle running to around 400 lines and 3,000 words, these themes are obviously explored in some detail.
Pope was quite religious, and the poem uses arguments from classical and Enlightenment philosophy to argue that the existence of God can be deduced from reason. To be technical he uses the teleological argument and the argument from necessary being.
The poem also uses philosophical ideas to discuss the nature of man himself. The main thrust of Pope's argument is that happiness is based on moral virtue rather than worldly gains. Likely influences are the Roman thinkers Seneca and Horace.
This really is a huge poem and it's very difficult to do much more than skim the surface in a general analysis essay. If you can it's best to focus on one aspect of the work. This will let you go into much more detail and demonstrate your knowledge of it, which generally means a better grade.