The Book Ethical Studies by Robert Bowie explains things really well. I would reccomend you get the book if you haven't.
What it says about Utalitarianism in the Summary:
-Jeremy Bentham devised the Utilitarian theory. Human beings are motivated by pleasure and pain [hedonism] and all humans persue pleasure, which is good, and seek to avoid pain, which is bad.
-The Utility Principle: the rightness or wrongness of an action is determined by its utility or "usefulness."
-Usefulness refers to the ammmount of pleasure or happiness caused by this action
-"An action is right if it produces the greatest good for the greatest number"
Hope that helps. The book has quite a bit more stuff which I'm not going to type out.