Skellige islands is one of the main parts of the game world. In contrast to Velen and Novigrad, you don't gain access to it after visiting the White Orchard and Royal Palace in Vizima. Reaching the islands is a bit more troublesome and you can deal with it during the Destination: Skellige quest. Important - You shouldn't start that quest before you reach around 14-15 experience level. Otherwise you might have trouble with winning a pretty hard and mandatory battle in which you will participate during the sea travel (details below).
Start by going to Free City of Novigrad. More specifically, you must reach its western part. There are a few ships there. You should be interested in the one shown in the picture above. Talk to Liglad on the deck of that ship, he will send you to his employer.
Captain Wolverstone can be found in the tavern near the port. You must talk to him and, sadly, pay him 1000 crowns for the trip (the game doesn't allow you to lower the price in any way, even with the Axii sign).
Important - if you don't have enough crowns, then sell items you don't need at local merchants. You can also try to visit Vivaldi banker and take a loan from him or exchange some currency (orens and florens for crowns).
The sea trip to Skellige islands won't be boring. During the journey you will be attacked by pirates. They are the reason why it was recommended to develop Geralt - otherwise he could have been too weak to eliminate the enemies (they are on 15 and 16 experience level). If you haven't listened to the warning and you're on much lower experience level then try to avoid staying in one place on the deck, look for opportunities to kill pirates that are fighting your allies and help yourself with the crossbow, bombs and witcher signs.
VERY IMPORTANT - The game forces you to rent the captain's services only during the first trip to Skellige islands. After that you can use quick travel to move around the whole game world (White Orchard, Velen, Novigrad, Skellige) with the basic (and free of charge) signpost mechanism. You don't have to worry about Roach as well, your horse will appear at the beach when you reach Skellige islands.