There are generally 2 events that lead to speciation- geographical isolation and reproductive isolation. In the first case, something occurs to split a population into pieces: a river changes course, a mountain popfines up, etc. This results in the second event, in which the parts of the population can no longer interbreed (there is a barrier to gene flow). As mutations accumulate in the pieces of the population and those new populations are subjected to different selective pressures, they start to evolve in different directions. After many generations, they are so different geneticaly (and otherwise) that they can no longer produce viable offspring.

This is what happened to the squirrels that live on opposite sides of the Grand Canyon; they were originally one species, but once they were divided by the Colorado River and, eentually, the Canyon, they evolved into separate species.