The Happy Mask Shop is located it the Market square of Hyrule Castle. The shop remains empty until after you have completed the Dodongo’s Cavern dungeon. Return to Hyrule Castle and enter the Happy Mask Shop (shown in the screenshot below) to pick up your first mask, the Keaton Mask.
The Keaton Mask needs to be delivered to the guard in Kakariko Village near the gate leading up to the Death Mountain Trail. Equip the mask and then speak to the guard and he will offer to purchase the mask off of you for 15 Rupees. Return to Hyrule Castle Market to hand in the 10 Rupees to the shop owner and pick up your next mask.
The Skull Mask needs to make its way back to the Lost Woods. Before you actually sell the mask to one of the Skull Kids in the Lost Woods, you can use the mask to imitate a small scene part of the way into the Lost Woods. Return to the grassy area and wander around near the back of the grassy area until you find a hole and drop into it.
The hole is located near the group of butterflies. Put on the Skull Mask and approach the lit up area. This will cause all of the Deku Scrubs to surround Link. Wander around until you find the leader. The leader will provide you with Deku Sticks and will enable Link to carry up to 30 of them.
The Skull Kid who wishes to purchase the Skull Mask is located near the front of the Lost Woods. Take the first left as you enter and step on the lit up tree stump. Speak to the Skull Kid and he will marvel at Link’s new mask.
He will then offer to purchase it from Link for 10 Rupees causing you to lose money on the sale. Return to the Happy Mask Shop with the “proceeds”.
Travel to Kakariko Village and enter the village in the daytime. Walk over to the Graveyard and find a small child wandering around. Speak to the child while wearing the mask and he will offer to purchase the mask for 30 Rupees. Return to the Happy Mask Shop afterwards.
The Bunny Hood cannot be sold to the person who wishes to buy it until after you have completed the Inside of Lord Jabu-Jabu’s Belly dungeon.
Hang around outside of Lon Lon Ranch and search for the Running Man around Hyrule Field. You can usually find him on the west side of the field. Speak to him while wearing the hood.
The Running Man will completely fill whichever wallet you currently own, therefore it is a very good idea to have already obtained the Giant’s Wallet from the House of Skulltula side quest.
Return to the Happy Mask Shop and pay back the 50 Rupees for the Bunny Hood. Now that the masks have all sold out, you will have access to the Mask of Truth, which you can use to speak to Gossip Stones throughout Hyrule. You can also borrow a Zora Mask, Goron Mask and Gerudo Mask from the Happy Mask Shop at any time.