First of all, you should talk to every single person in the town. Be sure to talk to the people behind the counters of the Flower Store and the Livestock Store. You'll get a watering can and a bag of grass seeds. After that, the shipper will offer you a ride back home. That should be your very first day.
On the second day, when you first get out of the house, you'll encounter a dog. This is Ellen's dog. She'll tell you that she can't have a dog in her house and then offers it to you. Name the dog. Once you do, you can keep it anywhere. It doesn't matter where you put it, but be sure to bring it inside when it rains, snows, or any other bad weather. After that's done, you should quickly run to the mountains and grab one or two wild grapes (or a herb if you have the time).