I feel that I'm an educated person, and I try to keep up with politics in America, but I really don't understand our system. How can some states be called with less than 20% of the votes being counted?
As to why so early, they have enough confidence in exit polls and other previous polls to say that, for example, Hillary is not going to win Oklahoma.
Those making a call will typically check how well the results for the counties that reported results so far correlate with the polls and historical results, guesstimate what that would mean for the other counties, and call it when they think the result is clear (hopefully, they employ statisticians to make the call, but even then, it remains an inexact science)
For example, if a state has had over 90% votes for party P in all its counties in the past ten elections, the polls say that won't change, results of ten percent of counties nicely distributed over the state in terms of city/countryside, rich/poor, race, etc. show it hasn't changed, making the call that P will win is easy. Everybody would take that bet.
For an example of 'calling it' going wrong, see https://en.wikipedia.org/wiki/Dewey_Defeats_Truman.