Deconstruction is one type of literary theory. Basically, it is one method that you can use to analyse any text. Deconstruction was at its peak in the 1960s, so I might suggest choosing a work from that era. Many poems by Lawrence Ferlinghetti lend themselves well to deconstruction. If you would like to learn more about deconstruction, read the works of Jacques Derrida, specifically "Of Grammatology". You might want to read an overview of the work first. It is challenging. The films of Jean Luc Goddard are also made to be deconstructed. Also, consider the art of Andy Warhol.
I think all works of art are subject to deconstruction in the sense of approaching the function of contradiction in the given text. To read a text deconstructively is to read it against the grain, upturning its operative hierarchy and showing how the text cannot evade its own upturning. However, it is interesting that in the Avant-Garde tradition, where the literary texts are deconstructive in themselves in the sense that they deplete an existing binary on their own, the deconstructive criticism in those cases faces a kind of redundancy e.g. Derrida referring to the impossibility of deconstructing Samuel Beckett's texts in Acts Of Literature interviews. According to derrida, Beckett's texts are auto-deconstructive.
All major 20th century writers--Eliot, Joyce, Hughes, Heaney, Borges, Calvino, Yeats, Beckett, Pinter can be read with deconstruction. The important theoretical texts would be Derrida's WRITING AND DIFFERENCE, OF GRAMMATOLOGY and the works of Christopher Norris, Hartman, Foucault and Lacan.