The serious answer is, just like humans.
http://static.discoverymedia.com/videos/components/apl/0feff55728e055122e803e078fd52aad07b6c910/snag-it-player.html?auto=no

That's impressive video. I wouldn't be surprised if orangs could walk 10,000 miles in a hundred years; that translates into a casual saunter across the landscape of about a hundred miles a year. More realistically, humans made it from Alaska to Tierra del Fuego in a thousand years, about 10 miles/year. Where low water levels or raised land create a bridge, they can walk there. If they can hang on to a fallen tree or plant mats, they can float there, perhaps swept down a river and out to sea by a big storm.

Don't forget the selection effect. It might be that millions of orangs got swept out to sea and simply drowned. It would only take one mating pair to survive to establish the species on an island.