Infusion — for leaves and flowers
Hot water poured over the material and left. Suits anything thin and aromatic: mint, chamomile, lemon balm, lemongrass, rooibos. Most tolerate five minutes and boiling water without turning bitter, which is the main way they differ from tea. Delicate flowers are the exception and want water off the boil.
Decoction — for roots, barks and hard seeds
Simmered in water rather than steeped, for ten minutes or more. Anything dense needs this: ginger, turmeric, liquorice, cinnamon bark, roasted roots, star anise. Steeping them produces a thin drink and the conclusion that the botanical is weak, which it is not.
Cold infusion — for anything you are not in a hurry for
Several hours in the refrigerator. Standard for Japanese mugicha and Korean corn silk tea, and excellent for hibiscus and butterfly pea. It extracts less bitterness and is very hard to get wrong, which makes it the most forgiving method here.
With milk or fat
Turmeric in milk, chai simmered with milk and spice, rooibos taken with milk in South Africa. Some flavours carry better in fat than in water, and where a tradition prepares something this way it is generally worth following rather than substituting water.
How to tell which you need
Look at what you are holding. If you can crumble it between your fingers, infuse it. If it is woody, a hard seed, or a piece of bark or root, simmer it. If it has been roasted, simmer or infuse long. Nearly every mistake in this category is a decoction being steeped.