How to brew black tea

Black tea is the fully oxidised leaf: picked, withered, rolled and left to turn dark before it is dried. That oxidation is what gives it its colour, its body and its tolerance for boiling water — the one kind of tea that wants it.
The short version
Water: freshly boiled, 95 to 100°C. Leaf: one teaspoon of loose tea, about 2 grams, or one teabag, per cup. Time: three to five minutes. Those are Whittard of Chelsea's figures, give or take its 95 to 98°C; the difference between that and a kettle that has just clicked off is a few seconds' pause.
How long for which tea
Whittard's three to five minutes covers the robust teas, and where in that range a tea sits is a matter of how it is made and how you take it. A sound place to start:
Assam and breakfast blends: four to five minutes. Malty, strong and built to carry milk.
Ceylon: three to four minutes. Brighter and a little lighter than Assam; good with milk or with a slice of lemon.
Kenyan: three to four minutes. Fast to colour and brisk — most of the strength in a supermarket teabag comes from Kenya.
Darjeeling: two to three minutes, which is what Whittard gives all its delicate teas, and cooler water for the spring picking. It is the exception among black teas and has a guide of its own.
Earl Grey: three to four minutes. Any longer and the bergamot turns from perfume to soap. See how to make Earl Grey.
Bitterness
A bitter cup of black tea is nearly always one of two things: it was left too long, or the teabag was squeezed. The tannins come out late in the brew and come out fastest under pressure. Take the leaf out on time and leave the bag alone.
Milk, lemon or neither
A strong Assam or breakfast blend is made for milk. Ceylon goes either way. Darjeeling and the lighter teas are better without: milk flattens the very thing you paid for. Lemon and milk together curdle, as anyone who has tried will tell you, once.
Second infusions
Western-style black tea gives most of what it has in the first pot; a second is usually thin. The exception is good whole-leaf tea brewed in the Chinese way — a lot of leaf in a small pot, short steeps — where three or four infusions are normal.
How to brew black tea: questions
What temperature should water be for black tea?
Freshly boiled, 95 to 100°C. Black tea is the one kind of tea that wants water at or very near a full boil.
How long do you steep black tea?
Three to five minutes: four to five for Assam and breakfast blends, three to four for Ceylon, Kenyan and Earl Grey, and two to three for Darjeeling.
How much loose black tea per cup?
About one teaspoon, or 2 grams, per cup.
Source: Whittard of Chelsea, Brewing a Cup of Tea checked against the source
More tea guides

How to make a proper cup of tea
The British cup of tea, made properly: freshly drawn water at a full boil, three to five minutes for a strong black blend, and the milk question settled — or at least explained. With the Royal Society of Chemistry's method and the ISO standard for comparison.

How to brew Darjeeling
Darjeeling is the black tea that rewards a little care: about 80°C and three minutes for the spring first flush, boiling water for the summer second. What the flushes are, how the gardens themselves brew them, and why the name is protected.

How to make Earl Grey
Earl Grey is black tea scented with bergamot: freshly boiled water, three to four minutes, and not a second more. Milk or lemon, how to make a London Fog, and what is known — and what is merely told — about the Earl.