How to brew green tea without making it bitter

Green tea is heated soon after it is picked, which stops the leaf oxidising and keeps it green. In Japan the heat is usually steam; in China it is usually a hot pan or a drum. Either way, the leaf that reaches your pot is more delicate than black tea, and the commonest way to ruin it is to treat it like black tea.
The short version
Water: 65 to 80°C — never boiling. Time: two to three minutes. Those are Whittard of Chelsea's figures, and a good place to start. Leaf: Whittard's teaspoon, about 2 grams, per cup. The Japanese way is quicker and stronger: Ippodo, the Kyoto tea house, brews its everyday sencha with 10 grams of leaf to 210 ml at 80°C for sixty seconds.
Why not boiling water?
Boiling water pulls out the bitter, astringent compounds in green tea fast, and scalds the sweet, savoury flavour that is the reason to drink it. If you have no thermometer, do what Ippodo does and pour the water from one vessel to another: by its reckoning, boiling water poured once into a cup and then onto the leaves is at about 80°C, right for sencha, and three transfers bring it to the 60°C that gyokuro wants.
Japanese green teas
Steamed, often finely cut, and brewed quickly. Sencha, the everyday Japanese tea, wants 80°C and about a minute — see how to brew sencha. Gyokuro, shaded before picking, wants cooler water still and a little patience: Ippodo's standard brew is 10 grams in just 80 ml at 60°C, for ninety seconds. Matcha is not steeped at all but whisked: how to make matcha.
Chinese green teas
Pan-fired, usually whole-leaf, and a little more forgiving. Whittard's two to three minutes suits them in a pot; in China they are as often simply left in a tall glass and topped up as you drink. Dragon Well is the famous one, and has a guide of its own.
More than one infusion
Good green tea gives two or three infusions, often four. The second is usually brewed a little hotter and much faster than the first, because the leaf has already opened.
How to brew green tea without making it bitter: questions
What temperature water for green tea?
65 to 80°C, by Whittard of Chelsea's figures — well below boiling. Boiling water makes most green teas bitter and astringent.
How long should you steep green tea?
Two to three minutes, by Whittard of Chelsea's figures. Japanese teas are brewed quicker and stronger: Ippodo brews sencha for sixty seconds.
Why does my green tea taste bitter?
Almost always because the water was too hot or the tea was steeped too long. Cool boiled water to 80°C or below — pouring it into a cup and then onto the leaves does most of the work — and take the leaves out on time.
Source: Whittard of Chelsea, Brewing a Cup of Tea checked against the source
More tea guides

How to brew sencha
Ippodo's method for sencha, Japan's everyday green tea: 10 grams of leaf, 210 ml of water at 80°C, one minute, and every last drop poured out. How to cool the water without a thermometer, and what shincha is.

How to make matcha
Matcha is green tea that is whisked rather than steeped. Ippodo's method for a bowl of usucha: 2 grams sifted, 60 ml of water at 80°C, fifteen seconds' brisk whisking. Thick koicha, a matcha latte, and the mistakes that make it lumpy or bitter.

How to brew Dragon Well
China's most celebrated green tea, from the hills around West Lake in Hangzhou, brewed the way the grower Mrs Li brews it at home: 4 to 5 grams in an open glass at 85 to 90°C, sipped and topped up all day. And why the tea picked before Qingming costs so much more.