Back at the Lannister camp, Tyrion is given his orders: he and his clansmen will be placed with the least disciplined soldiers in the vanguard (the front of the army).
Since his father basically puts him in a position to die, Tyrion goes to his own camp to be with Bronn, his squire Podrick Payne, and the new camp follower (Shae) that Bronn found for him. ("Camp follower" is a broad category of civilian who helps out the army; but here it's a polite way to say prostitute.)
But the next morning, Tyrion is rushed into battle: the Stark army seems to have surprised them. There's a big battle that the Lannisters win. (Tyrion survives, but a lot of others don't.)
Tyrion confronts his father about putting him in a bad place: Tyrion only survived because his clansmen fought better than they were supposed to.
But they've got worse news: apparently Robb Stark wasn't here, but has gone elsewhere with the main force of his army. Where?