The black teas of your distant memory may reside somewhere near the fond mental lobes that contain grandmothers, mothballs, and orange-infused-blends of tinned tea joined by little milk pitchers. Or perhaps they're more contemporary, among the ranks of food-service-grade teabags served with water that seems almost supernaturally hot. Your black tea experience need not dwell here forever: a well-steeped cup of black tea can be yours to savor unadulterated by creams or chipped china—unless that's, you know...your cup of tea.
What we call "black tea" is known in much of Asia as "red tea"—referring more to the color in the cup than the blackened appearance of the fully oxidized leaves before brewing. It may also be useful to distinguish between the origins of black teas, such as Chinese (whose leaves are picked earlier and withstand more oxidation) and black teas of other origins, e.g. Africa, India and Sri Lanka (whose leaves are picked later and are less oxidized). The difference in processing methods of these teas is reflected in their flavor, and affects the way in which you may choose to brew them.
That said, black teas can be brewed with just as much ease and versatility as any other—which is to say, go ahead and throw some in your gaiwan. A clay yixing pot is also a fine way to experiment with black teas, though you'll want to dedicate a specific yixing to heavily oxidized teas like these—or even one specific type of black tea—since the pot is intentionally crafted to take on the flavors of the tea brewed in it over time.
No matter what the black tea you're steeping, you'll use a hotter water than for most other teas—just off the boil, so somewhere around 195-205 degrees F. (This means if you're using a gaiwan, you are oh so much more likely to scald yourself with any spilled tea, or even as you grip the vessel, so this would be a great time to really perfect your technique!)
For Chinese black teas, you can go ahead and fill the gaiwan with a generous dose of tea, filling the vessel about 1/4 full. Rinse the tea and dump the water, then refill with water and steep for 1 to 2 minutes. These teas can be reinfused up to two or even more times if the tea is particularly young, with your time parameters being adjusted to taste.
For the other black teas, a smaller dose and longer steeping time are generally warranted. You may measure a teaspoon of leaves per 6 to 8 oz of water, rinse the leaves, and then steep for between 3 and 5 minutes. You'll know where you prefer to end the extraction by the depth of flavor and level of astringency you like best.
As with all tea journeys, the final cup will tell you what you like most about each black tea, whether it's malty, creamy, orange, caramel or bright floral earthiness. Feel free to take all steeping guidelines as simply a beginner's road map, and play around with your time, dose and temperature...and try not to burn your tongue.