Since there is no resort to resort transportation you have three options.
The first one is to take a taxi from your resort to either the Beach or Yacht Clubs. The second option is to take a bus from any theme park to either resort.
The best (IMHO) option is to plan on either the Disney Studios or Epcot the day (and time of day) you need to get to the Beach/Yacht clubs. From the Epcot World Showcase you can exit at the International Gateway, which is near the United Kingdom and has the same operating hours as the main Epcot entrance. From this exit the Beach Club is about a five minute walk. Keep going straight and the resort comes up on your right. The Yacht Club is another couple of minutes from the Beach Club on the same walk.
From the Disney Studios you can also walk but this will take about 15 minutes or so. You also have the option of taking the Friendship boats that run between the Studios and the Epcot International Gateway throughout the day. The boats are slow but relaxing. They stop along the route at the Swan/Dolphin, Boardwalk, and the Yacht/Beach clubs.