Steaming cooks food via the heat from steam.
This is a little bit like double-boiling except it does not need a ceramic double boiling jar and the container is not half-submerged in the water of the bigger pot.
The ingredients and the soup is placed in a soup bowl which can be ceramic or enamel. The bowl is then placed in a big pot above boiling water and steamed. The pot can be a big wok or a big stock pot.
Cooking with steam is not as common as simmering and quick boiling but it is a good technique for ingredients that are quite delicate and may disintegrate with agitation, for instance, fish.
My paternal grandmother loves to cook and she has this huge 3-tier food steamer which she would use to steam all sort of yummy food. However she rarely uses it to make soup. Instead, she would use the rice cooker or a big pot or a wok on the stovetop.
It is however possible to cook small petite bowls of soup using the chinese tiered steamer like Joyce Chen J26-0054 6-Quart 3-Tier Chinese Steamer

Do note that water should be brought to the boil first before the soup bowls are placed into the steamer.
How do you position the soup bowl inside the bigger pot or wok?
There are some accessories in a chinese kitchen that I have no English names for. One of them is this item below used to prop up bowls or tureens during cooking. The closest I could think of is a tripod.

It is a metal structure with 3 legs that you place at the bottom of the big pot or rice cooker to act as a pedestal for the soup bowl.
If you do a lot of cooking with steam, a tripod is a more convenient and safer tool than a plate. Chinese grocery shops or supermarkets should stock these.
If you cannot locate this little tripod, use a plate. Invert the plate and place it at the bottom of the wok or pot. Place the soup bowl on top of the plate.
2011 Update
I found a few tripods at Amazon and predictably, they are not called tripods.
- Chrome plated steel footed wire plate steam rack, size 10"
This rack has long legs and is suitable for use with deep pots.
- 5 5/8" Kitchen Cookware Stainless Steel Wire Steaming Rack Stand
This rack has very short legs and is suitable for use with tiered steamers or woks.
How do you remove the soup bowl from the bigger pot or wok?
Another one of those kitchen accessories that I couldn't find an English name for is what I would like to call the plate grabber. It is a very convenient and safe way to remove the soup bowl from the piping pot. It is also very cheap and can be found in asian grocery shops.

2011 Update
I found a 2-arm plate grabber at Amazon. It is Helen Chen's Asian Kitchen Stainless Steel Plate Retriever Tongs. Tongs isn't really the right term for this but well, I have to admit that it is a challenge translating chinese cooking utensils. This is what it looks like.

Soup recipes using steaming
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