Design
The seed of a new sculpture can be anything. A polyhedron (cube? disphenoid?), a thumbnail sketch gone right or gone wrong, a concept (larva lamp!), a knot in some string, a Pokémon, an actual seed. It's rare that a model starts in the computer, but it's happened.

Unless it's so galvanizing that I leap straight into CAD, I'll likely spend some time sketching, or getting smelly with plasticene. At this stage it might not look like anything: I'm trying to approach something that I can't see (I'm a haptic thinker and don't visualize easily), and probably couldn't model by hand if I could see it. I'm looking for a sense that there's something interesting lurking in the neighborhood. There may be grues.
At some point, out of curiosity or frustration or divine certainty, I switch into CAD, which for me still means Rhinoceros. I've stayed with Rhino this long partly from inertia, but partly because I think it actually does what I want unusually well.
To digress a moment, there are several types of 3D design programs. Boolean modelers work by adding and subtracting geometrical primitives, and they're great for working with existing components, and for modeling machining and fabricating processes. If you want to build a robot, Solidworks will help. Mesh modelers work by deforming a closed surface – a blob – without rupturing it. They're the closest approach to virtual clay, and they are terrific for freeform sculpting such as character models. If you want to make exquisitely detailed monsters, ZBrush is perfect. I have it; I use it.

Surface modelers, such as Rhinoceros, let the user define shapes by sending spline curves through space, lofting surfaces across them, and sewing the surfaces together into solids. It's a labor-intensive, unforgiving workflow, but it delivers a high-energy balance between freedom and precision. The splines and surfaces, mathematically generated from control points, have a purity that hand drawing rarely achieves. There's nothing to prevent clever topological tricks, but you must understand what you're doing completely to get away with anything good.
Rhino is also friendly to algorithmic work, having a command line(!), a native scripting language, and a plug-in API. If I want to put on my programmer hat and write a utility, a generative framework, or just a file format converter, it's no problem. This capability has been more and less central to my work at different times.
Do I use scanning? No. It doesn't work well on heavily undercut objects, which are the only kind I have.
I typically spend a lot of time in the CAD phase of a new piece: weeks to months, between midnight and dawn. I'm a very slow modeler, and I'm at peace with that. I am pretty sure the bottleneck is think time rather than hardware or software, so I don't stress about it as long as work is getting done.
Manufacture

I design mostly for direct metal printing. There's a machine that takes a file of data describing a 3D object, and builds the object out of steel. Although we call it a print, it's not a picture on paper. It isn't a casting, although it's made of metal. There's no plastic in the final piece. The machine doesn't cut the shape out of a block of steel, it builds it up out of powder. Let's imagine that this is real, and go forward from there.
Let's also imagine that since 2003 I've explained this thousands of times. Sometimes I sound like a bad science fiction writer, other times like an overenthusiastic slummer from beyond the Singularity. One good thing about the 3D printing media bubble is that it's gotten a little less uphill: at least people know what a 3D print is now.
I don't own a steel printer. They're large and expensive, and need a lot of skill and attention to operate. Ex One invented it, and they do all of my printing and most of the postprocessing.
The material is stainless steel powder, laid down in layers, held in place by a laser-activated binder. You can see the layering in the finished pieces. The powder feels like cool, heavy flour. During the build the extra unbound powder supports the piece, so no extraneous structure is needed to handle undercuts. Afterwards the loose powder falls off the part easily. It's flowable, rather than caky like cornstarch.

Once the part is built and depowdered, what's needed is to get rid of the binder and fill that space with more metal. Both are done in one step, infiltration, with heat. The secondary metal used to infiltrate my parts is bronze. Other combinations of metals than steel/bronze are possible, but none are yet available to me for production.
An uninfiltrated part is matte gray, feels like sandstone, and won't take a polish. It's soft enough to cut fast with a hacksaw, but can't quite be dented with a fingernail. During infiltration, what makes the bronze flow through the part? Capillary action, so they tell me. If you find this implausible, you're not alone.

The end result is a composite metal without porosity, with metallurgical properties between steel and bronze. It's springy and has good memory, like work-hardened bronze. It can take a polish or a patina, developing rust and/or verdigris depending on the environment. In a household environment it is usually fairly stable.
The color varies from quite bronzey to almost steel grey. Occasionally I get a batch that finishes out pure copper, as if it's been flash plated.
Chasing
A raw model is far from a finished sculpture, but from here on there's no interesting technology, just old school art.
First the infiltration stems ("stilts", as they're called in-house) are cut off, and if possible retextured. Then parts are tumbled in an abrasive medium to cut down the surface texture, then a burnish medium to give some polish. Before or after tumbling as desired, a chemical patina or heat treatment can be applied to darken and color the metal.
I used to do this at my studio, but about 2008 Ex One brought the postprocessing in-house, hiring sculptor Glen Gardner as resident technologist, and now they do a great job with it. I still hand-finish and sign some of my larger pieces, for old times' sake.
This is the most exciting thing to happen in metal since lost-wax casting was invented. That was over 5000 years ago, and this is going to be better: it's part of the glorious Cambrian explosion touched off by computers meeting art. What a time to make sculpture!
Other Materials
Even so, one need not live by metal printing alone. Sometimes I add magnets, glass, ball bearings, or other fittings after parts are printed: for functionality or a color break or pure whim. I have a small fusing kiln to make the glass how I want it.
Through Shapeways I also offer many other materials: ceramics, lots of plastics, semiprecious and precious metals. (These last aren't made by direct printing, but by casting from wax prints.)
Designing for these materials has very different constraints and quirks than for metal printing, but generally I'm able to adapt. I have a pre-technological studio art background including lots of casting, and I worked with many types of 3D printing before Ex One's process came online. It all helps.
The golden rule of 3D printing is that the designer must adapt to the technology. It can feel like magic, but it's only another art medium, no more universal than oil paint or lost-wax casting. For me the way forward has always been to listen to the tech, and the people running it, asking sincerely what it can do, what it can do that is new.