Water is arguably the most important ingredient when preparing a good tea - otherwise excellent teas can be let down by poor quality water or simply water of the wrong type. After the tea leaves themselves, temperature is the other big influence on the resulting flavour.
The main factors that influence the flavour of water are its mineral content, its pH or whether it is slightly acidic or alkaline, and the amount of air dissolved into the water.
Mineral content is often the main issue affecting water quality. It is often known as the hardness of the water and is usually down to the amount of calcium and magnesium that has dissolved into water while it percolates through limestone or chalk deposits. Hard water is not a problem from a human health perspective, but it presents all sorts of challenges both from an engineering perspective and for the issue of flavour quality.
If you live in a hard water area you will no doubt be familiar with many of these challenges, from the buildup of limescale on taps to the damage done to boilers and pipework. The effect on tea is for the taste of the dissolved minerals to crowd out the more subtle notes found in high-end teas and to cover up the main flavour profile of any infusion.
There are two ways to address this - one is to select a tea with a rich, powerful flavour that can cut through the hard water taste. Black teas from Yunnan or Assam are a good option for this, but of course these are not to all tastes and in order to cut through the hard water they will have to be infused strong, losing much of the subtlety that they could offer. The other option is to filter the water. A good active filter system can remove most of the hardness from water, and this doesn't have to be an expensive plumbing fitting. It can simply be a jug style filter designed to provide a surface for the mineral content to bind to. Essentially this simply allows the mineral content to come out of the water as limescale, leaving a naturally softer water behind.
The other water quality issues are less of a concern and are much easier to address. Water pH is very closely linked to mineral content, with hard water being more alkaline. It is also quite common for municipal water suppliers to treat their water to make it slightly alkaline to prevent corrosion of pipes. This can be addressed in the same way by filtering the water if it is causing quality issues, but is not often extreme enough to need correcting.
Dissolved air content is a factor in the taste of water itself, but it isn't an issue when making tea. As water is heated its ability to hold dissolved gases reduces and the flavour is changed. This can be proven by simply taste-testing fresh cold water from the tap against boiled water that has been allowed to cool. The result will be the water that has been boiled coming out tasting flat and lifeless. Getting water up to the temperatures needed to infuse any kind of tea will remove most if not all of the dissolved air from it, though, so there is no impact on the resulting flavour of the tea from this.
The main water purification method to avoid is distillation. Distilled water is completely free of any mineral impurities and is of the ideal neutral pH, but these imperfections are only a problem in excess. Lacking them entirely goes too far in the other direction and results in a flatter, less interesting tea infusion.
After water quality and the quality of the tea itself, temperature and infusion time are the two biggest factors affecting a tea.
The first thing to do is to start with fresh cool water. Using pre-heated water from a tank or boiler might seem like it would save time, but water sits for a long time being kept warm and can pick up a metallic or mineral taste from the tank or pipes. This is especially an issue with commercial coffee machines which usually store hot water in copper tanks that are particularly prone to leaving water with a metallic taste.
The next step is deciding how hot the water is going to get before making the tea. This doesn't have to be complicated, but it often helps to consider whether the water should reach a full boil or whether it only needs to get up to around 70° or 80°. Different styles and types of tea benefit from different water temperatures and this can be controlled either by mixing boiling and cool water in the teapot or more accurately by using a variable temperature control kettle.