While Robert's away hunting, Eddard gets to play… king. He sits in judgment, hearing people's complaints. And the first complaint is quite a doozy. (Also, the Iron Throne is made up of old swords, so it's not comfortable and has no place to put a remote control.)
It seems that someone is raiding Tully land (or the land of someone who owes allegiance to the Tullys). One of the witnesses says that it was definitely Gregor Clegane; even without any symbol or banner, it's easy to tell it was him because he's so big.
Edmure (Cat's brother) wants to fight back, but Eddard thinks that will make the Tullys look like they started it. (Basically, politics here is like politics on a playground.)
So Eddard puts together a group of warriors under the command of Ser Beric Dondarrion. Eddard sends Dondarrion, Thoros of Myr, Ser Gladden Wylde, and Lord Lothar Mallery (and a bunch of soldiers without names) to go stop Clegane.