Sketches, plans and scale models
Some woodworkers take inspiration from the materials themselves: they pick up a plank and think "this would make for a nice cabinet door", and they build the piece adapting every shape and dimension to that piece of wood, often the protagonist of the work. A great example of this was James Krenov, who used to work improvising along the way from a vague idea.
I almost never do that. In fact, I find risky to get my hands on the wood without having put all my ideas into detailed plans and having a mental view of the procedure I'll be following. Here are some of my resources:
Pencil drawing of a nightstand in front elevation and isometric perspective. This drawing contains almost no technical information, but helps getting an idea on the appearance of the real object. I prefer not to color it, so colors can be made up in the imagination.
Here, one of my favorite methods: Sketching on metric paper. It is a very clever way to get a quick sketch that maintains proportions and can actually be used as a plan. This one shows different views on the joinery of a stool and a cut list.
A Sketchup 3D model for my tool cabinet. It can be very effective with straight lines, but i find very difficult to work on curves, especially compound curves. There are more refined softwares in this field, such as 3D Studio Max, but they are rather complex.
I built this 3D model of a client's bedroom from the architect's plan to have a preview of the furniture scheme. We finally chose different items and distribution. I've never been in the actual room, so that was helpful.
If plans and drawings are not quite sufficient, a plywood model can be very effective. The curves for this wall mirror are designed freehand, so a mock up shows us wether the 2D design has any appeal on three dimensions. What the mock-up doesn't show is the beauty and texture of the wood. This design is awaiting among many others to become an actual thing - I'll keep you posted.
I should mention CAD plans (I love AutoCAD): they are supposed to be the most versatile and efficient tool, but I always find myself with a pencil in my hands. Lack of habit, I guess.