Green tea is famous for its high level of antioxidants. Green tea is by far one of the most popular tea styles, with thousands of incarnations of it, ranging from fruity green teas to spicy green teas. It is less oxidized than black and oolong teas, and care must be taken in the steeping in order to not scald the leaves.
Water temperature: Not quite boiling. You want the water to be fairly hot, but not boiling. Boiling, or just-boiled water will scald the delicate leaves, giving you a bitter tasting cup of tea. If you boil the water, do let it cool a bit before preparing the tea.
Steep time: Much like black tea, the length of time the leaves are left in the water varies by personal taste. However, steep times for green tea, on average, will be longer than steep times for black tea.
White tea, while less famous than green tea, in fact has the highest antioxidant count of any tea, primarily coming from it being the least oxidized of any tea. The leaves are extremely sensitive and tender. However, a well made cup of white tea should be quite smooth and refreshing.
Water temperature: Hot. If you see small bubbles form in the water as it is heating, it is definitely hot enough.
Steep time: White teas typically have long steep times. Some, in fact, can be left in the brewing vessel indefinitely, like oolongs.
Rooibos, or rooibus, is not technically a tea, containing no actual tea leaves. Instead, in contains leaves from the African red bush. Rooibos come in a very wide variety of flavours. Naturally sweet, it is often consumed for its antioxidants or as a refreshing midday drink. Rooibos typically goes quite well with lunch.
Water temperature: Boiling.
Steep time: Indefinite. The leaves can be left in as long as desired with no danger of a bitter cup.
Maté is another non-tea, instead being the leaves of a South American plant. It has a high caffeine content and is drunk many places in South America as an alternative to coffee.
Water temperature: Boiling.
Steep time: To taste. Various mates taste better stronger. It is usually an experiment, to find the optimal taste for optimal steep time.
Containing no tea at all, these are typically blends of flowers, spices, fruits, and other herbs. If you can think of it, it has probably been turned in to a tisane, the name for a blend that is infused in hot water to make a beverage.
Water temperature: Boiling.Steep time: To taste. It is hard to mess up making an herbal. If it tastes too strong after you have steeped it, add more water. If it is not strong enough, steep it longer. There is really no limit, except your own personal preference.
I hope you enjoyed this brief primer on tea. Please do not hesitate to comment with any questions you might have. Feedback is also appreciated.