In the old day, whiskey distilleries in Scotland would be built near a source of pure water (that’s why there are so many of them in such out of the way places as the Highland and the Hebrides). Master distillers knew that, water being the main ingredient of whiskey; they needed the best water to produce the best whiskey. Yet, whiskey is only 60% water, while the water content of tea is probably over 99%.
Without good water, you simply can’t make good tea. If you water tastes of chlorine or contains one of the numerous chemical that are mixed with the water supplied to city dwellers to make it “fit for human consumption”, then your tea will also, even if the chemical taste is somewhat obliterated by that of the herbs and spices you have brewed. To make good tea, you need good water.
The best water for tea is fresh spring water. We are lucky enough, at home, to have a spring well in our back garden. Our water is gently gravity fed from it, and whenever I drink tap water in town, it taste like detergent in comparison. Rainwater (and probably melted snow as well), is very good too. Bottled spring water is dead, because it is no longer being oxygenated, but it still is better that city tap water. If possible, choose one with a low mineral content and a neutral pH (read the label on the bottle). If you must use tap water to make tea, then at least buy a good filter, which hopefully will eliminate some of the chemicals, but don’t fool yourself, you won't make good tea from bad water, no matter how much you filter it.

Teapots

The first thing you will need is a good teapot. In fact, unless you never drink tea in company, it would be better to have two or three, of different sizes. One small one containing one or two cups for intimate tea drinking, and one or two larger ones, containing four or more cups for social occasions. Generally, tea is better freshly made, and with a few teapots you can always make the right quantity.
All teapots are not born equal. A good teapot should hold the heat and therefore be heavy enough for this. The best materials are probably Earthenware and China, if they are not too light. I have also come across excellent Japanese cast iron teapots. Stainless steel and glass teapots are generally too light.
It should be easy to pour the content in a cup without spilling it everywhere, and if possible, this should be checked before you buy it. I have at home a beautiful Balinese teapot in the shape of a tortoise. It is however perfectly useless as it will pour more tea on the table than in the cup you are aiming for. The top opening should be large enough, to make it easy to fill and clean the teapot, and the lid must have some kind of “locking" mechanism that will prevent it from falling, and breaking, when you are pouring. Finally, it should, if possible, look nice.

Other essentials

One of the most important kitchen accessories for serious gourmet tea brewing is a serious mortar and pestle. Choose yours with care, as it will have to withstand heavy pounding when you are crushing a dry root of liquorice or turmeric. For that reason, only a cast iron one or a heavy stone one will do. Wood is not hard enough, and a China one might crumble under heavy use. I have a heavy cast iron one, which I bought for a few cents in India (where mortars and pestles are treated seriously because they are needed to grind spices). It is small, surprisingly heavy and incredibly tough.
I have already mentioned tea strainers. Stainless steel ones are best, but for that purpose, plastic is acceptable. Choose one with the finest possible mesh; it is most annoying to be eating wet dust when you just want to be drinking tea.
Of course, cups or mugs of some description are also essential, but choosing them is mostly a matter of taste, so the only advice here is to make sure that you have enough of them.

Brewing

For reasons of convenience, you will probably use an electric kettle. These are fine except for one detail: they usually over boil the water. They should be switched off when the water starts to simmer, rather then when it is boiling heavily. Not a big problem if you are nearby, lending an attentive ear to the process. Boiling the water in a pan over a gas hob is better, however.
In most cases, the teapot should be warmed up before hand. (However, some herbs, like green tea, prefer a cold teapot.) Pour out all the water used to warm the pot, and boil another kettle. Or warm the empty pot on the stove or a radiator, which has the advantage of keeping the teapot dry, and saving water and electricity. Then mix the various herbs and spices you have selected for today's brew in the empty pot and pour the simmering water over it.
Brewing time is important. The optimal brewing time depends on what goes in the brew. Green tea, for example, shouldn’t be brewed for more than a three minutes (it will get bitter if brewed for two long). Liquorice, on the other hand, needs ten minutes to release its sweetness fully. Usually between two and five minutes is fine.
“Tea balls”, made of stainless steel mesh, are available. They are convenient, but using one means that you can’t stir the brew before serving it, and they might be too big or too small, so tea strainers are far better because of the flexibility they offer.

Serving

Serve the brew when it’s ready, not before, and not after. Stir the content of the teapot quickly before serving.
In some North African and Eastern countries, tea is poured into the cup from a great height, the narrow drip of hot liquid cooling down on the way. Very elegant if you can manage it, but can be messy…
The habit of adding milk and sugar to tea is born amongst a people who drink such low quality stuff that it might have been the best way to make it palatable. Furthermore, strong black tea brew is astringent and heating, which is somewhat balanced by the addition of the sugar and milk, so it make sense in that case. But generally speaking, adding milk, sugar, or honey to your brew is not recommended and only detract from the real taste. Adding milk to mint tea, or honey to a brew containing liquorice would simply be absurd.