Suppose a seamount forms from an underwater volcano. Birds on the mainland colonized the island. How might this lead to speciation?
This seamount, will supposedly to have speciation occur, would have a sustainable ecosystem, of sorts, with a possible development of plant life in the fertile soils, as well as possible development of coastal habitat such as reefs to provide food in the form of fish.
Due to these sustainable, conditions, the birds will stay here.
However, due to random mutation, certain individuals in these species will survive better than others, with the more desirable characteristics and adaptations to survive.
Those birds carrying these will survive better than those who do not, and will see a gradual reduction in the numbers of those of the species who do not have those said characteristics as they die off due to being out competed.
These birds will eventually look very different to their ancestors, and will be perfectly suited to this isolated islet's lifestyle.
If it is more woodland, the birds will develop beaks suited to the prime food source, whether that be nuts, in which the bird will develop the muscles and a large beak to crack the nuts, or for insects, insect beaks are often more pointed and narrow to be able to 'pluck' and hold the bird's prey. They will also develop narrower wings, due to the need to move quickly with great agility around the tree canopy and floor. They may also develop better eyesight to deal with the lower lighting.
If it is more sea orientated, and they nest on the cliffs, developing eggs which are more elliptical, so they do not roll off the cliff. They may also develop more pointed and perhaps slightly serrated beaks to hold fish more easily.
I Hope this helps and can encourage you to think of other scenarios.
For example, and island with goats on it is suddenly split in two, the northern island becomes colder, and the southern island becomes more arid and dry.
Now think of the characteristics these goats may develop due to being separated and the adaptation which will occur. Same process, just different scenario.