With leaf tea you throw the leaf away. With matcha you drink it: the powder stays in the water rather than dissolving, which is why the technique matters more here than it does with a pot of sencha. It is also why it takes about a minute to learn.
What you need
A bowl wide enough to whisk in, a bamboo whisk, and something to measure with. A chawan is wide and shallow so the whisk can move; a mug is too narrow and the powder collects in the bottom corner.
A chasen has fine split tines and that is what creates the foam. A milk frother works and gives a different, larger bubble. A fork does not.
Sift it first
Matcha clumps in the tin, and a lump will not whisk out. Push the powder through a small sieve into the bowl before you add water. This is the step most people skip and it is the reason most home matcha is lumpy.
A matcha tin with a built-in strainer does this in one motion.
Usucha, the everyday bowl
Sift 2 g into a warm, dry bowl. Add about 80 ml of water at 80 °C. Whisk briskly in a W shape for around 15 seconds, keeping the whisk near the surface rather than scraping the bottom. Stop when there is a fine, even foam.
Drink it straight away. Matcha separates within a minute or two, which is not a fault, it is powder in water.
Koicha, thick tea
Twice the powder and half the water: around 4 g to 40 ml. You do not whisk this into foam. Knead it slowly with the whisk until it is smooth and glossy, closer to thin honey than to tea.
Only a ceremonial grade will do this well. At this concentration a culinary grade turns bitter.
Matcha latte
Whisk 2 g into 50 ml of water at 80 °C first, then pour that into 150 ml of hot or cold milk. Doing it in that order is what stops it from clumping, because matcha does not disperse in milk the way it does in water.
Any milk works. Oat foams best of the plant milks.
Iced matcha
Same as the latte, but pour over ice at the end rather than mixing with warm milk. Use slightly more powder, because ice dilutes as it melts.
If it goes wrong
Lumpy: not sifted, or the water was added too fast.
No foam: whisk too slow, water too cool, or the chasen is worn. A whisk that has lost tines will not foam.
Bitter: water too hot, or a culinary grade used for drinking. Drop to 70 °C and see what changes.
Dull green rather than bright: the matcha is past its best. It will still work in a latte.
Looking after the whisk
Rinse it in warm water before and after use, never with soap, and let it dry on a stand with the tines spread. A chasen that dries flat splays and breaks. On a stand it lasts several times longer.