For bagged black tea, I use a kettle to boil water, pour it over the bag in a 15 oz mug, and steep for three minutes. If you don't have a kettle, a microwave works fine (contrary to what snobs say), but be aware that it will be hotter than you'd get from a kettle because it also heats the mug. If the tea is bitter, cut the heat and steep time. If it's not strong enough, adding more tea leaves is ideal, but adding heat or steep time can also help.

Edit: I don't agitate tea as it is steeping but I imagine it would have a similar effect to increasing steep time.