I am making vegetable soup for about eight people and would like to cool it in little time. Refrigeration seems to be a good choice, but I would like to know if there are better methods/techniques out there.
Put a bunch of ice in your sink or in a container large enough to place your soup pot in. Add enough water to cover the ice. If the soup pot is large or wide, you can speed up the cooling by periodically stirring it: this is particularly important for thicker soups or stews, where the middle section of a pot can stay warm for a long time. Or, for maximum cooling, break up the soup into smaller -- preferably more shallow -- containers first and then place them in the ice bath (though this isn't generally necessary if you're using ice).
If you don't have that much ice, you can use a cold tap water bath to at least get it down to near room temperature before refrigerating. But you will need to replace the water frequently for fast cooling.
(Unless you're breaking up the soup into smaller containers first, I would strongly recommend an ice bath over simply putting a large pot in the refrigerator. It can take many hours for the contents of a large pot to cool completely in a refrigerator, which can be a food safety hazard. If you do use the refrigerator alone, put into smaller containers and don't stack them to allow air circulation, and obviously don't place them next to highly perishable foods like raw meat, etc.)
I usually let soup cool at room temperature for 15-20 minutes in a wide, shallow, very thermally-conductive pot or pan set on a cooling rack. A large saute pan works well. Moving it to a different vessel than the one the soup was cooked in leaves behind all the heat retained in the cooking vessel, especially if you're making soup in something heavy like enameled cast iron. With lots of exposed surface area and occasional stirring, it's cool enough to store pretty fast. I put it in containers and refrigerate it while it's still warm.
An ice bath is about as good as you're going to do. And if you're really serious about the speed of cooling, then don't forget the trick of adding salt to the ice bath - a bath of water, lots of ice, and lots of salt (when well mixed/agitated) can reach a much lower temperature than just water and ice (all the way down to -4F (-20ºC) if you're good!)
As an alternative plan, you might leave some of the water out of the recipe (if possible) and put the equivalent amount of ice directly into the soup to cool it later. I think this will cool the soup even faster than the ice bath because the heat exchange situation will work much more quickly than the relatively limited conduction-heat-transfer area between pot and ice bath.
If you want a literal answer to what's the fastest way, I say pour in some liquid nitrogen.
As to fastest practical way, I too would recommend not using any active cooling technique while the soup is above 50°C. In particular, refrigeration is a really bad choice, because you introduce a lot of heat into the refrigerator which it will have to work hard to get out again. It's a big waste of energy. While the soup is hot, the heat will happily go away itself if only you give it some path to escape. One good way, as suggested by Dan C, is to use a big surface area. In particular, that takes away a lot of heat through vaporisation.
Another useful technique is to put the soup in the sink in a closed pot and keep cold water running all over- and around it for a couple of minutes.