There is a house that is across the road from someone I know that has been abandoned for a while. The yard is out of control. If I were to move in there and start living there and cleaning the place up. What legal action will the owner have against me if they show up?

You would be a trespasser. You would be thrown out. You could also be sued for fair market rental.

They could be put in jail for criminal tresspass, it is possible they would have trouble proving what property in the home is there's and lose a lot of it.

A home belongs to someone, what you do, go to the register of deeds and/or property tax office and see who owns it and who the tax bill is going to and try to buy it from them.

You can not just move in and expect to live there.