How do I factor quadratics?

The simplest way I can put it is that you find two numbers that multiply to the constant term that also add up to the coefficient next to x.

i. e. x^2 - 8x + 7. This would factor to (x-1) and (x-7) because - 1 • - 7 = 7 while - 1 + (-7) = - 8.