There are a variety of means, some of which can still be practised easily today. The simple answer is that tinder is collected, which is then ignited by various means to catch fire. This is then used to start the fire in the fuel available. Said fuel varied based on whatever was available.

At its most primitive, two sticks can be used to start a fire. The first, larger stick would have a hole bored through it using an awl. The second would then be inserted into the hole at a right angle, and the tinder placed beneath the hole. By rubbing the stick quickly to rotate it, it would use friction to heat the wood and eventually produce embers. These embers were dropped into the tinder, made of quick-burning material such as dry grasses or wood shavings, and the fire was stoked by breathing on it. Once the tinder was alight, it would be introduced to the prepared stack of wood or charcoal. Source: Primitive Technology by John Plant.