Follow the tutorial and you'll get there.
If I recall correctly first one is to collect 3 stones which you can get by mining outside mine located above the forest that is above the village center.
After that, you have to obtain 10 wood which you can get above the village center and the map that is above your house.
Afterward, you have to order some material in the tool shop you get during the 10 wood.
Then you go to sleep get the material in the mailbox outside your house if I'm not mistaken and talk to Walnut again.
I think that should be the final one that unlocks most of the buildings. If you don't know on which one of those you are talk to Walnut the lady that greets you after arriving on the island.
A suggestion in case you'll be lost what to do in the game Ummm I guess you could say story-wise you can have one of the companions in your party and on the menu select
View attachment 672285
and Speak
Selecting that will give you a rough idea of what you're supposed to be doing in order to do the "quest" sometimes the description or translation maybe both is weird however it's better then nothing.