I find poems to be the best way to tackle and anaylsis question. The way to look at them is in a series of steps.
First off I look at the poem as a whole, what is the general message and feeling of the poem. Are there any obvious aspects that you can notice, a rhyming scheme or rhetoric? What is the poem's structure.
After the overall view look at each stanza one by one, how are the sentences or lines strucutred, what is the point of each stanza and why has the poet chosen to arrange it in this specific way.
Are there any words that stand out to you or phrases that catch your eye. Look at the senses the poet has used in things like colour, textures and smells. These are all important aspects of the poem.
Finally try and bring all the information together to give your view on what the poet intended to achieve and what message you took away from it.