Hiring a captain
The quest will start automatically after finishing the main quest Royal Audience in which you will meet with all the most important characters in the Royal Palace in Vizima. In order to take care of this quest, you must go to Novigrad and it is recommended to start completing it AFTER you reach about 15-16 experience level. Otherwise you will have serious trouble with completing the large sea battle described below.
In this quest you must find transport to Skellige Islands. There won't be many people eager to take you there. Go through the road pointed by the quest and ask various ship captains whether you can rent a boat. You will learn about a captain (M6,6) who can be found in the inn. He will agree to take you to your destination. However, it will cost you 1000 crowns.
Journey to Skellige
The road won't go without an adventure - the ship will be attacked by pirates. You won't be fighting long before the ship crashes on the rocks. You will wake up at the shore. A Skellige man, thanks to whom you have awaken, will tell you some interesting things. You can also get in a fight with him if you use aggressive words. Then go to the city to meet with Yennefer. The quest will end and another one will start: The King is Dead - Long Live the King, which is the main plot at the Skellige Isles.