What do I do with all the items I pick up?

Similarly like the bugs, you can use the treasures to upgrade your items at the Scrap Shop in the Bazaar or sell them to Rupin, the Gear Shop owner at night.

To upgrade your items, go to the Gondo, the Scrap Shop owner at the Bazaar to see which items can be upgraded. He will list which treasures you need and how much rupees it costs to upgrade an item.

Otherwise you could sell your treasures to Rupin, the Gear Shop (where you can buy shields) owner at his home at night. He will only offer to buy 4 different treasures from you at any given night. So if he doesn't want to buy a certain treasure you want to sell, come see him another time and he'll probably be buying.