Why don't we begin with the easy one. Black tea is far and away the simplest to brew and very few individuals run into any real difficulties making a tasty cup. Basically, use 100 ºC water and steep the leaves for a couple of minutes. This method will work well for Assam tea and pretty much any of the widely consumed Chinese teas, Ceylon teas or Nepalese teas. Darjeeling tea, however, is made using a different process. It should be prepared employing colder water (80-90ºC or 180-194ºF), owing to the fact that it is only somewhat oxidized and essentially very similar to an oolong tea.
Green tea is not as easy to prepare the correct way, given the large variance of different types and the large inconsistency in the method of brewing. The appropriate water temperature and the steeping times are the two factors you really need to pay attention to. 80°C (176°F) is the preferred temperature for preparing the majority of green teas.
One exception is the exceptional quality Japanese tea gyokuro, which calls for a colder water temperature of 50°C–60°C (122°F–140°F). The Japanese tea Houjicha, which is roasted, is another exception. Perhaps the most difficult tea to screw up, it can simply be made employing 100°C water. The guidelines printed on the packaging will suggest a good time to start in terms of steeping times. Otherwise, try starting with a minute and a half for gyokuro and two minutes for all other teas.
Ignore all that above, if you're brewing Matcha green tea powder; it is very different from all the other green teas. Since it is a powder, it necessitates a unique and pretty complicated method of brewing, which includes special gear. Matcha is the tea featured in the Japanese tea ceremony and if you've ever seen one done, you are familiar with how involved it can get to prepare matcha. I would prefer not to ramble on for the length of a major novel, so I'll leave off delving into any details on the way of brewing for this very high quality tea.
White tea can be a bit more difficult to brew properly, too. The leaves are very delicate, so it requires a much lower water temperature than green tea. The correct range for both White Hair Silver Needle and White Peony is 75-80°C (167-176°F). When it comes to steeping times, try 2-3 minutes and vary until you're happy with the result. If you prefer a stronger cup of tea, add to your steeping time; if you like your tea less astringent, subtract from the steeping time.
The most difficult kind of tea to brew well, excepting matcha, is oolong tea. The traditional gongfu style of brewing requires many quick infusions using a heap of leaves. Not to worry, however; you can prepare oolong teas by sticking to standard methods and they will taste wonderful. Take care to watch the water temperature: it has to be just a little below the boiling point.
No doubt you're thinking the instructions I've given are quite a bit basic. Of course, to prepare the best tasting cup, you'll need to make use of the guidelines for the specific type of tea. If you don't have those, however, using my instructions will result in an enjoyable cup of tea, no matter the type. Hopefully, this should embolden at least a couple of men and women who have in the past determined they can't stand tea, to give it another taste. I am certain you'll be grateful you did.