On your third day, crafting is unlocked. You can upgrade your house if you haven't already.
On the morning of your third day, Victor and Nigel will visit. Nigel will tell you about crafting, and will tell you how to upgrade your house.
With crafting unlocked, you can create different types of Makers, which you can use to make useful and valuable materials. Be sure to look at the Makers in your crafting list and try crafting them when you have the materials.
Upgrade Your House
When possible, go to Nigel's Handiworks and ask Nigel to upgrade your tent to a log cabin. The log cabin includes many useful features that make farming easier, such as a bath to restore stamina (it uses 30 minutes of in-game time per bath), a refrigerator to store food in, a kitchen where you can cook, and the ability to have a pet.
Getting a Pet
After you upgrade your tent to a log cabin, go to the Hoof House Animal Shop in Olive Town. The first time you visit the Animal Shop after upgrading to a house, you will get a leash for free. Then you can purchase a pet from Bridget in the Hoof House Animal Shop. You can use the leash to take your pet for a walk. You can get more pets by upgrading your house further at Nigel's Handiworks. The general store sells pet treats that you can feed to your pets, and toys that you can throw for your pet to fetch while you take your pet for a walk outside.