This is a tough cookie, I'll do my best :)
First of all, the four terms formalism, structuralism, post structuralism and new historicism are methodologies used to analyze literature.
In formalism, the tendency is to analyze text in terms of its style, nee, its form. The techniques used, the mechanics, everything concerning the taxonomy of text is the focus. The way in which the text was put together (say, for example verses versus prose, etc) is another focal point.
In structuralism, literature is reviewed through patterns. It is the conglomerate analysis of text that tends to show similar behaviors. I would say that Jane Austen can be interpreted under a structural analysis because her novels tend to show similarities in the making of the characters, and the telling of the story.
Poststructuralismis an answer against structuralism, or better yet, an addendum to structuralism which claims that it is hard to analyze text under the structural method when authors will always tend to use their own interpretive practices, borrow styles, and interdepend on each other's talents.
In other words, Jane Austen and Charles Dickens were contemporaries so easily one could have "borrowed" any form of skill or style from the other as part of their own writing processes, so you cannot just isolate them as separate writers.
This is what takes us to- New Historicism
This fascinating methodology aims to re-discover history by using both context, culture and general knowledge in order to put together a revised version of historical events in real-life description.
For example, instead of examining the poetry and writings of Shakespeare as a genius accident of the times, they take minor writings, collect historical information of the time, look into lesser-known Elizabethan actors, and ALL the information surrounding the times of Shakespeare.
The findings of these types of researches show that historians have many times just given a pedestal to historical characters and attribute some unique qualities to them that are simply not as unique.
The artist and his or her art are a symptom and a product of their time and society, therefore, what Shakespeare did may not necessarily be the works of a genius, but writings done as a result of his circumstantial possibilities like many other writers do.