Field & Stream magazine has the definitive guide on how to start a fire without a match. This one is the classic "rubbing two sticks together" method:
Rubbing two sticks together is likely the oldest of all -fire-starting techniques, and also the most difficult. Besides proper technique, you have to choose the right wood for the fireboard and spindle. Sets made from dry softwoods, including aspen, willow, cottonwood, and juniper, are preferred, although a spindle made from a slightly harder wood, combined with a softer fireboard, can also work. The friction of the spindle against an indentation in the fireboard grinds particles from both surfaces, which must heat to 800 degrees F before a glowing coal forms. This must then be transferred to tinder and -gently blown to life.