Through natural selection it happened over many generations and it was gradual, not a sudden change in the founder species. One bird was randomly born with a fatter beak and so could eat a seed that was harder to crack, this meant he lived longer than the other birds or was fitter, so bred more and so more of the offspring had this slightly larger beak. This continued and the birds moved to the islands with their ideal seed and kept getting fatter beaks etc until they were no longer the same species (this is when they can't breed to produce fertile offspring).
