How should I begin to analyse an unseen poem?

Firstly, read the question carefully, highlighting any key words i.e  'power' or 'nature' if it is thematic or ' structure' or 'metaphor' if it is technical, to keep in mind when reading the poem.
Keeping these key elements of the question in mind, read through the poem. Try and assess what its subject matter is.
Now, read it again. Highlight anything immediately striking (and, importantly, relevant to the question!) and try to annotate it, so you have handy notes that can be turned into full and well composed sentences later on.
Find at least three points of analysis on each of the following areas: form, structure, language and theme. 
Find a good point to begin with, maybe it will reference a quote from the beginning of the poem, or maybe it will discuss the broader context to begin with. Either way, make sure you let the examiner know the areas that you will be focusing on (form, structure etc). 
Now, follow your structure set out earlier, and in each section make sure you are following the PEEL technique, making a point, providing evidence (relevant quotes), exploring their relavance and explaining it thoroughly, then linking it back to the original point you were making.
Keep in mind throughout this the theme or question that you were asked to consider - it is important to ensure that you are answering this question, not another you may have had in mind. 
To conclude, read over the rest of your essay and consider the main point of its argument, what it is that is connecting your points, and condense this into a few sentences for a strong final point. 
Read over your essay again for clarity, pat yourself on the back and move on to the next question!