Deconstructionism is a technique of literary criticism which seeks to analyze a work as thoroughly as possible as it pertains to other works. In other words, acording to creator Jacques Derrida, "there is nothing outside the text" (Wikipedia) because every written source is in itself a linked text; Derrida believed that there was no objectivity possible. The main aim is to understand why the work was created, by examining the "context" of its creation: history, era, culture, society, and other similar works.
To analyze a poem using deconstruction, the first step should be to place down the superficial meaning; what do the words say? How does the poem speak to you? Most examination of poetry focuses on the surface meaning without digging deeper. You should try to find out where and why the poem was written, and for what purpose: was it a response to cultural norms, or a reflection of self-examination? Who was the writer, and why was this poem, at this time, so important?
The historical context is also important. Many poems directly reflect public sentiment of the time, while others deliberately go against the popular sentiment. Use your knowledge of the writer and his/her lifestyle to understand how the poem reflects the times.
Check the links below for more detailed information. Deconstruction, as Derrida explains, is not a step-by-step process, but rather an intuitive inspection of elements as they form a whole; perhaps you could pass in a draft paper and get the teacher's input.
Deconstruction is, yes, contextual (read belarafon's comment). But more importantly there are several things he misses touching on.
Deconstruction suggests that one entertains all the possible meanings of the text, and that one treat the text as itself, rather than some singular intended meaning to uncover (Specifically, an emphasis on these qualities lead to the development of New Criticism).
In addition, deconstruction discovers innate paradoxes in the text. If they are self-refuting the deconstructionist exposes them as such, and if they are self-supporting then the deconstructionist outlines the structural integrity of the oppositions.
Deconstruction is both analytic and anti-analytic, separating things into their parts, but attempting to recognize irreducible qualities, qualities which resist analysis.