In the book Hoot, what did Roy's father help him with?

Roy's father, Mr. Eberhart, helps his son in two very important ways.  First, he helps Roy to decide what he should do about an injustice about which he feels very strongly.  And then, when the decision is made, Roy's father uses his resources to provide Roy with some very important evidence to expose the parties against whom Roy is fighting.

Roy gets himself in deep trouble when he allows Mullet Fingers to check into the Emergency Room at the hospital using his identity.  When Roy is caught and must explain to his understandably angry father, he tells Mr. Eberhart the whole story leading up to what happened at the hospital.  Mr. Eberhart listens to his son "without interruption", and seriously considers what Roy tells him about the endangered owls whose habitat will be destroyed if the construction of Mother Paula's Pancake House is allowed to proceed.  Seeing that his son is involved in a very serious situation, he reprimands him for when he has acted irresponsibly, but also takes very seriously his son's concern for the injustice that is about to take place.  Mr. Eberhart recognizes that his son is growing up, and that the problems he is facing do not have easy solutions.  After giving his own perspective on different aspects of what is going on, he acknowledges that he himself does not know the right answers, and suggests that they both "spend some time thinking seriously about all this".  Mr. Eberhart treats his son with respect.  He trusts Roy to make reasoned decisions, and will support him in whatever course he decides to take (Chapter 13).

Once Roy has committed himself to stand up for the preservation of the owls, Mr. Eberhart helps in more practical ways.  He writes a note to get Roy out of school so that he can attend the protest that will take place at the groundbreaking of the construction project, advising Roy only to "be careful...and be smart" (Chapter 19).  And finally, Roy's father, realizing the validity of the cause in which his son is so passionately involved, taps his own resources and does some research of his own.  It is Mr. Eberhart who discovers the important evidence - the missing Environmental Impact Statement - that exposes the illegal actions perpetrated by the people behind the construction of Mother Paula's Pancake House and saves the endangered owls (Chapter 21).