The finer the grain, the quicker the brew time as the surface area of the tea exposed to the hot water is greater. Nearly powdered teas are ready to go in about two minutes or less, while large leaf varieties may need more than five minutes. The general rule is three to five minutes, blacks longer than greens. The longer a tea steeps, the more likely it is to become slightly astringent or "bitter" to the taste. Some tea lovers prefer a bit of astringency, while others recommend putting the tea into infusers or paper filters (rather than directly in the pot) as the leaves can more easily be removed from the pot after the prescribed steeping time, which also preserves a bit more "virtue" in the leaves if the intent is to reuse them to brew a second pot.
With black teas, the hotter the water the better. Bring it just to a boil and let it back off a couple of degrees. Green teas are usually a bit more delicate and do better in water that is in the 160 to 185 degree range, so it may make sense to let the water cool a bit before brewing the tea in this case. If you dont want to get out the thermometer, just bring the water up to a boil as usual and then take it off the stove, allowing it to cool for five minutes or so before pouring it on the green leaves.