Press B (or the bag button) to open your bag: 30 spaces. Right-click anything in it for what you can do with it; drag things to arrange them.
The tool belt
Under the bag hangs your tool belt: a place each for an axe, a pickaxe, a fishing net, a fishing rod, a harpoon, a sea rod, a hammer and a tinderbox. A tool on it works as if it were in your bag, takes no room there and stays with you if you fall. A tool you get goes onto the belt while its place is empty; right-click one in your bag and choose Hang on your tool belt, or click one on the belt and choose to take it off. A new character’s tinderbox, hammer and fishing net start there.
The pet pouch
Under the tool belt, once you have a pet: a pocket each for your companions. Click a pet there to call it or send it home. Pets & companions.
Stacks of 100
What you gather comes in stacks of 100, one stack to a bag space: logs, ore, raw fish and stone (logs, copper ore, raw shrimp, stone and the rest). Each time a stack fills, the work stops and the game says so: click again to start the next stack in a free bag space, or bank some. So nothing is gathered while you are away. A stack from the bank, a trade or the ground may be bigger. Other things that stack (coins, arrows, food) have no such limit.
Shops and your bag
A shop opens your bag beside it: right-click something in your bag to sell it, and use the amounts or Sell all for a stack. Close the shop (its ×, walking away, Esc, or another window) and the bag it opened closes with it; a bag you had open already stays. Close the bag and the shop closes too. The pet shop sells from no bag, so it stays.