The Sunstone - Skellige
This quest will automatically begin after you sail to Skellige during the Battle Preparations Quest. Depending on who you decided to help (or did not help) during the King's Gambit Quest <Add Link> in Skellige earlier in the game will determine who you have to speak to for the first part of this quest.
If Cerys or Hjalmar rule then you'll have to speak with Crach an Craite who is near the docks where your ship lands. If Svanrige rules then you'll have to speak with him in the King's Chambers of Kaer Trolde where he'll be signing a peace treaty. A fight will break out shortly after speaking with Svanrige and you'll have to kill all of the Nilfgaardians. After the scene he'll send you to Ermion right after.
You can find Ermion on the southern portion of the main Skellige island at Kaer Muire. Speak with him and Madman Lugos here and depending on the dialogue options you choose - you might have to kill Madman Lugos and his men. If you do kill Madman Lugos and his men you'll have to follow Ermion all the way out of Kaer Muire before you're able to speak with him.
Ermion will update your quest and give you two new objectives, speak with the Pearl Diver north of Arinbjorn or Eyvind to the west of Arinbjorn. Both of these objectives will give you the information that you need, the main difference between them is you can fail to get the information by visiting Eyvind.
When you arrive ay Eyvind he'll be looking for a giant white whale by the name of Moby Dick, rather, Gevorg. During you conversation with him you'll get two timed responses. It doesn't matter what you do during the first one (he'll miss the whale either way) but during the second timed response (pictured below) you'll want to choose option #2 "Gathering material for an adventure novel". He'll open up to you and tell you what you wish to know if you choose this option.
If you choose wrongly then visit the pearl divers (pictured below) to get the information you need. You'll find them inside of the under water cave right near their boat/quest marker.
Regardless of the route/option you choose when all is said and done you'll have to return to Kaer Trolde Harbor and speak with Yennefer to update this quest. She is still near the boat which you arrived on in the Battle Preparations Quest. There will be some dialogue here during which you'll receive the Child of the Elder Blood Story Quest. It's best for you to save this quest until last, it'll be required to complete the Battle Preparations Quest.
As for The Sunstone quest it will update and place a quest marker on your map on the northern portion of Ard Skellige where Philippa will be waiting for you. There is an Ancient Crypt Signpost you can fast travel to right at this location, otherwise you'll have to ride a boat up here.
Speak with Philippa then follow her into the ruins. You'll battle some monsters in here but for the most part the quest is fairly linear from this point forward. In the same room that you fight the Siren and Drowners you'll want to make sure to grab the Place of Power that is here. You can return for it later too if you missed it.
Eventually you will reach the room pictured below where Philippa lights up a crystal on the ceiling that shines light into mirrors around the room. In this room you have to go from mirror to mirror and pull the lever on the back. Each mirror needs to be moved a single time to complete this part of the quest.
You'll occasionally have to fight some Ghost enemies too in this part of the dungeon which mirror members of the Wild Hunt. Once you've exposed the Sunstone all you need to do now is head over to where Philippa is and there will be a scene.
Once you hear Philippa out the quest will complete. You can either go through the doorway right near where you spoke with Philippa to leave the dungeon or back track the way which we came. There is more to do in these ruins too if you're an explorer junky.