Forming
You can get leather to hold a shape by wetting it, fastening it to a "form" that's the shape you want it to take (usually carved from wood) and letting it dry. That's the basic technique, but of course there are all sorts of nuances and opinions on how to wet it, how to dry it, how to fasten it, etc. Forming usually is combined with other techniques as part of making a product.

Stamping
Stamping is straighforward enough in application; you have a stamp, a piece of metal with a design or image embossed on one side, and you put it against the smooth (grain) side of a piece of leather and apply strong, abrupt pressure, usually by hitting it. Usually stamps are mounted on thin metal handles about three inches long and as thick as a pen or pencil, or they're designed to be fit onto such a handle. Typically you hit them with a special hammer, with either a rawhide or polyurethane head. Typically you rest the leather on a special, hard flat surface. A lot of people like slabs of granite for this purpose.

Tooling
Tooling is done by cutting a design into the smooth side of a piece of leather with a special, very precise knife called a "swivel knife", and then following up by using a stamp-like tool to compress or push up the leather. Again, this is usually done on a hard surface, often marble. The cuts are very shallow and only penetrate the "grain" of the leather, the thin, smooth surface layer, without going much into the flesh of the leather.

Construction
I'm using the blanket term "construction" to cover the basic, conventional ways to build things out of leather. This includes cutting, skiving, strapping, sewing, lacing, braiding, gluing, rivetting, snapsetting and other inventive ways of handling leather.