In the Old Way, the end of the smudge stick or braid was lit from the council, central or cooking fire. Now we often use a candle. Matches aren't very efficient because it takes a while to get the stick smoking. In some cultures, pinches or even branches of herbs are placed directly in a camp or council fire, or onto the burning wood in an indoor fireplace. In other cultures, a coal is removed from the fire and placed in a special receptacle.
Most people use prepared, quick-lighting charcoal.
It's available from many Indian trading posts, at pow-wows, health food stores, new age shops, and even bible and Christian supply sores. The container used as a receptacle for your lighted charcoal and Sacred herbs needs to be fire-proof. Ceramic and glass bowls or abalone shells work well. There are also special chalices designed for smudging. Unless you use a chalice, place a layer of soil, sand or salt in the bottom for insulation, before adding your charcoal and herbs.