How to get the Zora's Flippers
After acquiring the Power Glove you'll have access to the northeastern portion of the Light World. In this area you'll primarily find Zora's River, Zora's Waterfall and the Waterfall of Wishing. Before you embark on your journey to get the Flippers make sure you have the 500 Rupees you'll need to pay for them.
Once you are ready to go you'll want to head northeast from Link's house towards the Magic Shop. On the eastern side of the Magic Shop you'll find a large boulder that you can now lift since you have the Power Gloves. If you're reading this after acquiring the Flute Fast Travel you can use that to be instantly flown to the Magic Shop.
Lift the boulder and follow the linear path - smashing the stacked rocks with your Pegasus Boots until you come across an area with a lot of water and a waterfall. For those that have never been here before, this is the Waterfall of Wishing. It's also commonly called the Mysterious Pond.
You won't be able to swim inside yet but you will shortly once you get the Flippers. Inside you'll be able to toss your Shield and Boomerang into the pond and upgrade them! It's very important you do these things - so remember to come back to this location after you're done!
Inside the waterfall is the Mysterious Pond.
To get the Flippers stay on the shallow water and follow it north as far as you can possibly go and then you'll want to start heading east. Eventually you'll come to a large waterfall with King Zora floating there. Speak to him and he'll offer to sell you the Flippers for a bargain price of 500 Rupees. Hopefully you took my advice and you came loaded!
King Zora isn't there in my screenshot since I acquired the Flippers earlier in the game - but I am standing at the location you'll find him. Also, a picture of where he is on the map for those interested.
Buy the Flippers and head south - grab the Heart Container which is a quick detour west before dropping down the Waterfalls and heading back to the Mysterious Pond.
Additional Note: The Zora's Flippers are an extremely important key item for you to get. It's required early on in the Dark World but arguably just as important - it's involved in a load of side quests and Heart Containers.