This page explains how to get all four bottles, which you can use to catch fairies, bugs, potions, and other things.
As a child, after you have met Zelda, go to Zora's Domain and win the waterfall diving game. Then dive into the underwater hole that takes you to Lake Hylia. Dive down to pick up the bottle that you can see underwater. Go to King Zora in Zora's Domain and use the bottle on him to show him Ruto's letter. King Zora lets you keep the empty bottle.
Go into the big house in Lon Lon ranch and talk to Talon to play the Super Cucco game. Find the three Super Cuccos and Talon will give you an empty bottle.
As a child, talk to Anju in Kakariko Village. Find her missing cuccos and throw them into the cucco pen, then talk to her to get an empty bottle.
Complete the Big Poe Quest to get the final empty bottle.