Metaphor is at the center of most poetic expression.  So, find what is referred to as the "controlling metaphor" and see to which the main idea of "The Burning of the Leaves" is being compared. 

Since a good poem creates a small world of its own, you may wish to discover the world in which the poem is set.

Basic analysis of a poem includes discussing the literary devices and poems theme.  Here is a link on how to analyze a poem.

http://www.enotes.com/topics/how-analyze-poem

Basically, you want to see what jumps out at you.  How does the poem make you feel?  What lines seem most meaningful?  What message is the poet sending?