How should I approach an analysis of a poem from my anthology?

There are two key things to remember when tackling one of the poems found in your anthology in order to achieve high marks. The first, and most important, is to have already prepared three or four cohesive points that you wish to address, that can support your overall argument. These can be thematic or formal in nature, and, although contrasts should be highlighted, should demonstrate an understanding of a cohesive message or quality that the poem possesses. Locating these should be done by locating evidence for them in the poem, which could come in the form of almost anything: from a complex rhyme scheme to a particular piece of imagery. Having collected enough evidence and derived your points from them, you have already completed the first two stages of PEEL (this is: Point, Evidence, Explanation, Link). Having outlined your point, you can then demonstrate the evidence and argue your case for its importance in the explanation. Following this, it is then always beneficial to link what you have written (or said, if it is an oral examination) to either another piece of evidence, or to your next point, to keep your argument fluid.
The second key aspect that examiners are very keen on is demonstrating a knowledge of the poet's ouevre and potentially even their life. Refer to the writer by name whenever possible, and remember to make connections with other poems in the anthology to show off your knowledge. In terms of biography, it is best to make educated deductions from what you know of the poet and the context in which they are writing, and avoid bold statements that leap to conclusions. If you do this, you will certainly illustrate the breadth of your knowledge, and your work will achieve high marks.