Strange as it may sound, cutting through stainless steel is not all that different from cutting through wood--with one or two exceptions, obviously. All you need is a good cutting tool--and many types of saws will actually work quite well in this instance--and a healthy respect for said cutting tool. Unlike cutting other types of metal, however, there are certain tools--oxy-acetalyne torches, for instance--that will not cut through stainless steel.
It may sound like some cool gimmick from a science fiction movie, but the plasma torch is actually one of the best, if not the best, metal-cutting tools available. Plasma cutters work by essentially directing a stream of gas, such as nitrogen, oxygen or other noble gasses, through a powerful electric spark called a "plasma arc." This spark superheats the gas until it becomes plasma, the fourth state of matter (others being liquid, solid and gas). The plasma becomes a directed stream from there, heated to around 16649 degrees Celsius and moving at 20,000 feet per second, it will simply melt or even vaporise the metal the instant the plasma comes into contact with it. Obviously, great care must be taken when using a hand-held plasma torch; but if you are planning on cutting through stainless steel and do not want to use any of the more conventional methods, you cannot go wrong with a plasma torch.
Snips are like a cross between scissors and industrial-grade bolt cutters. Typically designed with heavy blades, these are the most low-tech of cutting tools that can be used to cut stainless steel. They are generally only recommended if there is no other tool handy and the steel you are trying to cut is relatively thin. If you do decide to use snips, make sure you get a pair of "compound" snips, as these snips are designed to allow you to apply greater pressure on the metal as you are cutting, which in turn makes the cutting easier and able to go through heavier metal.
First of all, no, it is not a good idea to use your powered wood saw to try and cut stainless steel. Attempting to do so could damage the saw or injure you. There are, however, several different types of saw blades that have been designed specifically for the cutting of metal--and by association, stainless steel. Carbide-tipped circular saw blades, for instance, are more than capable of cutting through most metals, and many are specifically designed for jobs such as cutting through pipes and metal fittings. Jigsaw blades designed for precision metal cutting are also available and will allow you to cut sheets of stainless steel to exact specifications when used.