During the low season the ferry goes only to Djurgården (where you will find the Vasa Museum, ABBA Museum and Skansen) and you have to inform them that you wish to be let off at Skeppsholmen. The same goes for being picked up by the ferry at Skeppsholmen... there is a button at the dock you have to push to let the ferry captain know you need to be picked up. In the past the ferries always stopped at Skeppsholmen during the summer months, doing a Gamla Stan-Djurgården-Skeppsholmen run every 10-15 minutes.
...and to Fotografiska.
However... I noticed a slight change this season when I took the boat yesterday. Now they have one boat that runs only between Gamla Stan (Slussen) and Djurgården and another boat that makes more stops. This latter boat goes from Gamla Stan to Fotografiska (photography museum), then to Djurgården before the final stop at Skeppsholmen. I timed it and the whole trip took 20 minutes. The important thing is to ask, when you get to the dock, which boat is going to Skeppsholmen. It's nice that they stop at the popular Fotografiska during the summer as well!
Ferry at dock in Gamla Stan (Slussen). Picture taken last autumn!
There is also a bridge from the downtown area which takes you to the island. So it is an easy walk if you are near the royal palace or Kungsträdgården park!