Once you reach the farm with Shawn — depending on if you chose the day or night — Chet will take off for home and Shawn will introduce you to Hershel using the description that you told him when you met.
Once you are on the porch getting patched up, you have the choice of lying, being honest, or avoiding Hershel’s questions. Which you chose will come up later on when you have a conversation in the barn with him. If you were honest, he will be nice-ish about it. If you lied to him, he will call you out on it and be not-so-nice-ish about it.
Once you wake up in the morning and Clementine shakes the spiders out of her hair, you will meet Kenny and Katjaa. There won’t be any difference in the conversations and you will learn that Kenny has a boat, Clementine is in the first grade, and Katjaa was a vet.
When you go over to the fence where Shawn and Duck are, you can talk to Duck, look around, and help Shawn cut some wood. The actions here have no altered outcomes no matter which you choose. Shawn will also ask if you’ve had to kill any walkers yet. Whatever option you choose, it says that he “won’t forget that.” He actually will in about 2 minutes.
When you enter the barn to talk to Hershel, he will either reprimand you for lying to him the night before or just talk about the farm. If the previous night you chose to avoid his question by saying "you couldn't remember what happened to your leg," he goes easier on you and just calls you dishonest instead of calling you an outright liar, which he does if you told him you jumped a fence.
As soon as you are done talking to Hershel in the barn, the next big decision comes and what you choose will have a large impact. You will have to choose between saving Shawn or Duck, the immediate difference is that Hershel will tell you not-so-nicely to get off his farm if you chose to save Duck. If you choose to save Shawn, he will have a short talk with Hershel before dying. Hershel still kicks you off the farm, but is a little bit nicer about it. Even if you choose to save neither Shawn nor Duck and make no decisions, Hershel will still treat you the same as if you went to save Duck.