I would start by describing the stages of the revolution. It begins with the idealistic vision of Old Major. Then there is a stage of revolutionary talk, where the animals consider their current condition and the need for revolution. Then, there is the inciting event that leads to action, in this case when the animals are not fed so they break into the shed and the men attack them. Then the revolution occurs, and is followed by a period of blissful prosperity when the new government is being formed. Then it's all downhill from there!
The main tool to use to deconstruct this excellent novella is to identify how it is an allegory of the Russian Revolution and the massive comments it makes about Communism and ideologies in General. It would be well worth your time to investigate how Orwell uses his devastating work of literature to emphasise the horrors of Communism and to act as a critique of this ideology. You might want to consider focussing on how characters and events stand for specific historical individuals, groups of people and specific events.
I'm not exactly sure what your goal in deconstructing is, so this may or may not be helpful; however, the second most recognizable thing about Animal Farm (aside from its depiction of the Russian Revolution, as mentioned above) is that it's a fable. The elements of a fable (animals, human thinking and animal behavior, moral) give you some room for deconstructing this novella, it seems to me.
I think you are asking how you might pick this piece apart and look at what elements have been put together to ensure the book's ultimate meaning.
I would begin by looking at the characters who represent pieces of the Russian Revolution. We have great handouts here on enotes to clarify who is who and what they represent.
Then you might take a look at how each of the archetypes established might represent aspects of our current real world cultures. Do we still have Stalinistic Napoleon's in our world? Yes. Do we have Pravda/Sqealer media outlets that don't always tell the truth even though it is their job? Yes. Do we have intelligent Trotskyish Snowballs that are kicked out of places because of how much they know?
Do we ever run into problems as voiced by this book? Yes.
If you can clarify your question, I am happy to give you a clearer answer through a message.
You should divide up the book into different elements and see what you can mke from the individual pieces. For the plot, see what Orwell says about revolutions in general, not necessarily the Russian Revolution. Great works aren't that specific to one event but have universal enduring themes about the complexity of mankind and nature itself.