Bottles carry fairies, potions, milk, bugs, fish and Poes, and the remake has five of them instead of four.
If you only want the quickest route, do the Potion Shop, Lon Lon Ranch and Kakariko Village on your first trip through Hyrule as a child, pick up the Lake Hylia bottle on the way to Zora's Domain, and leave the Big Poes until you have Epona and the bow.
Empty Bottle #1: Hyrule Castle Town
Child era. New in the remake.
Head into the Potion Shop and you will see that a bug has escaped. Talk to the shopkeeper and he will hand you an empty bottle to catch it. Afterwards, he gives you a Red Potion and you keep the bottle.
Empty Bottle #2: Zora's Domain to Lake Hylia
Child era. You will need: Silver Scale.
Talk to the NPC at the top of the waterfall and win the minigame (collect all five scales) for the Silver Scale. Then swim through the underwater tunnel to Lake Hylia and dive for the bottle in the sunken ruins by the tunnel exit (it glints at night). It holds Ruto's letter: show it to King Zora and the bottle is yours (this is story-related).
Empty Bottle #3: Kakariko Village
Child era.
This is the reward for returning the 7 Cuccos to their pen in Kakariko Village (see the All Cucco Guide).
Empty Bottle #4: Lon Lon Ranch
Child era.
Head into the house on the left at Lon Lon Ranch and talk to Talon. Pay the 10 rupees and find his three Super Cuccos in the flock within 30 seconds. They stand and walk differently from the rest. The prize will be a new bottle filled with milk.
Empty Bottle #5: Hyrule Field to Hyrule Castle Town
Adult era. You will need: Epona & the Fairy Bow.
As an adult, ride over the logs in Hyrule Field that have purple flames around them. This makes a Big Poe spawn. Then shoot it twice with the bow and it will drop its soul. Bottle it and take it to the merchant in Hyrule Castle Town. The logs are very easy to see and there are 10 in total, but you only need 5 souls to get the bottle from the merchant. Here are 5 locations.
You then have to take a total of 5 Big Poe souls to the merchant in Hyrule Castle Town as an adult, and you will be rewarded with the bottle.

