Cutting - separating materials is done by physically breaking bonds, or more recently by melting. Cutting techniques have found particular favor with sheets of material, such as metal plates, metal sheets, fabrics, etc.
Metallurgical/Finishing - a variety of processes that do not significantly alter the geometry of the object, but are required for product performance or marketing. Consider heat treating processes that will heat a metal and change the properties. Or painting that makes a part more attractive and helps protect the metal surface.
Molding/Casting - Molding and casting technologies have been used for millennia, but they have recently begun to find interesting new techniques, and materials that expand the applications, and techniques. In general this method uses material in a liquid form, that solidifies into the shape of a mold.
Particulates - small particles of material have been used to manufacture low cost parts of complex geometry at high production rates. In effect a powder is put in a mold, pressed until solid, then heated to make it stronger. Materials include many metals, ceramics, glass, etc.
Forming - The idea of reshaping objects has been done for long periods of time (e.g. blacksmiths). Our knowledge of materials has allowed us to take advantage of subtle properties. Certain materials can be worked past the point that they would normally fracture. Materials can be bonded at an atomic level, and entire parts can be made out of a single crystal.
Joining/Cutting - By joining two or more parts we can create more complex geometries and assemblies. Consider parts that are glued or welded together. Parts may also be made by cutting larger parts into smaller pieces.
Electrical/Chemical - The transformational abilities of electricity have long been known (e.g. lightning), but it has only been controllable in the last two centuries. The ability to manipulate energy at the atomic level allows us to deliver highly concentrated energy, or manipulate materials one atom at a time. Most of these techniques use electrical potential, or flows to move, manipulate, and heat materials.
Fibre - By mixing two materials at a macroscopic level, we can obtain properties that are not possible from common materials. This technique basically involves taking strong strands of one materials, and embedding it in another material. Good examples of these materials are boat hulls, rocket fuel tanks and nozzles, fibre reinforced tape.
Rapid Prototyping - A newly recognized need is to turn out parts of correct geometry, and reasonable solid properties for testing of new designs, and sometimes production of tooling. These techniques typically make parts in layers, and allow complex new geometries to be built. The layers are often built with photopolymers that are developed with laser light.