Kinstone Fusions are a central side activity in The Minish Cap. Throughout Hyrule, you'll find various NPCs who have a Kinstone piece they wish to fuse. You'll also collect Kinstone pieces (red, blue, green, and gold) from defeated enemies, chests, and pots.
When you find an NPC with a Kinstone piece, talk to them and select the 'Fuse Kinstones' option. You'll then choose one of your Kinstone pieces that matches theirs. A successful fusion will trigger an event somewhere in Hyrule, often revealing a hidden chest, opening a new path, or causing a rare item to appear. There are over 100 Kinstone Fusions in the game, and completing them all is necessary for 100% completion and unlocking certain secrets. Pay attention to the shape of the Kinstone pieces; they must perfectly match for a fusion to occur. The rewards range from Rupees and Heart Pieces to new areas and even the Ocarina of Wind.