There are four Empty Bottles in The Minish Cap. Bottles can hold potions, fairies, water and more, and you'll need at least one early on, so the first bottle is worth picking up as soon as you can.
Cost: 20 Rupees. Requires: bombs and the Spin Attack.
Once you've learned the Spin Attack from Swiftblade, show it to the soldier at the north-west exit of Hyrule Town so he'll let you through. In Trilby Highlands, head south-west to a ladder and climb down. Bomb the cracked wall on the right to find a Business Scrub. Hold up your shield so the seeds he spits at you bounce back and hit him, and he'll agree to sell you an Empty Bottle for 20 Rupees. Make sure you have the money with you: you need this bottle to carry water to the beanstalk on Mt. Crenel.
Cost: free. Requires: a red Kinstone piece that matches Smith's.
Fuse Kinstones with Smith, Link's grandfather, at home. A cutscene shows a chest appearing in the Eastern Hills, near Eenie and Meenie's farm. Go there and open it for the bottle.
Cost: free.
Shrink down at a Minish Portal in Hyrule Town, cross the wooden beams into Stockwell's shop, and drop down behind his counter. Stockwell gives you a Bottle of Dog Food and asks you to feed his dog. Warp to the Lake Hylia Wind Crest and go into the red-roofed house nearby (Stockwell's House). Pour the dog food into the dog's bowl, and you're left with an Empty Bottle to keep.
Cost: free. Requires: completing the Goron quest.
Throughout the game, Kinstone fusions with Eenie and with the Mysterious Walls around Hyrule send Gorons to the Goron Cave at Lon Lon Ranch. Once all six Gorons have arrived and broken through the last wall, you'll find 200 Rupees in the first chamber. Climb past the Gorons to the altar room at the back and open the large chest for the final Empty Bottle.