How did animals get to distant places after the Flood?

Many people have trouble understanding how animals got to distant places around the world after disembarking from Noah's Ark. While it is likely that humans transported some animals on boats, this is not the only explanation available. Somewhat ironically, Richard Dawkins reminds of this when he writes,

"Most islands around the world, even quite remote ones like Ascension Island, have animals. Some of these, for example birds and bats, got there in a way that we can easily understand, without postulating a great deal of luck. But other animals, like lizards, can't fly. We scratch our heads and wonder how they got there. It may seem unsatisfactory to postulate a freak of luck, like a lizard happening to be clinging to a mangrove on the mainland which breaks off and drifts across the sea. Freakish or not, this kind of luck does happen — there are lizards on oceanic islands." —Richard Dawkins, Climbing Mount Improbable, W. W. Norton & Company, Inc., 1996, pp. 282