What are the pigs trying to do?
The major goal of the pigs becomes to manipulate and take advantage of the other animals' work and abilities. The pigs claim to participate in the betterment of the farm by using their brains, but that seems to be more of an excuse to the reader than the real reason. Based on the evidence of their lifestyle within the farmhouse, it would seem that they are using the other animals to fund their own entertainment and comfort. We know this to be true by the end of the book as the hens eggs are sold, Boxer is presumably sold, the wood pile is sold, and the pigs seem to be drinking and staying up late and rising late in the morning.
What the pigs are trying to do is different at different points in the book.
At first, the pigs are just trying to get a better life for all the animals. They are trying to overthrow Farmer Jones and then they are trying to set up a decent society once they do overthrow him.
But then the pigs kind of "go bad." Not long after they drive out Farmer Jones, the pigs start trying to take more and more power and privileges for themselves. Now, they are trying to become more like the humans that they used to hate.