Check Your Journal
Stardew Valley will often give you quests to do. These can be found within your journal along with a description of how you can complete them. To start, the game will give you some, but random ones may pop up to help the townspeople that you could accept if you’d like. These might be timed, and you might end up with a lot of them, so it’s good to check your journal to keep track. Not only that, but once you complete one of your quests, you’ll receive a reward and the only way to claim it is through this very journal window. So, yeah, make sure to keep checking back to it.