I have to illustrate a fictitious example of divergent evolution and I know the basic idea that a population splits to form two separate populations which then becomes isolated from one another and then different selection pressures and natural selection cause them to evolve differently.
But I'm slightly confused. Does variation occur within the population before it is isolated or after it is isolated? And must the two populations be geographiaclly isolated by a barrier or can they simply live at separate ends of an island?

Variations in nature will occur, independent of the situation. It's natural selection that makes the variations more visible, for example when the organisms are isolated in another environment.

Not necessarily. This can fairly well happen "at separate ends of an island" like you said.

I hope it helped!