The "human calculators" who don't have some form of savantism just utilize alternative methods of mental mathematics. One of the more well known human calculators Scott Flansburg wrote a book highlighting the "shortcuts" or alternative calculation methods.http://www.amazon.com/Math-Magic-Everyday-Problems-Revised/dp/0060726350
One of my favorites is 2 digit numbers times 11 it is super easy with little practice. for example to multiply 32 and 11 simply add the 3 and the 2 and put the result in the middle: 3 + 2 = 5 , 32 X 11 = 352 another example 51 X 11, 5 + 1 = 6 so putting the 6 in the middle you get 561. All of these "tricks" are found analyzing the patterns found in multiplication tables and other calculations.
That's the way I'd do it but I read math magic when I was a kid and it taught lots of simplifying strategies that I didn't learn in school