A very common method mentioned by woodnthings
uses straight pieces wide enough to get the curve to lay out within them. First draw out the pattern on 3/4" MDF or particle board and cut out and smooth the edges. Then cut straight pieces of wood that will fit on the pattern allowing for enough lengths to do scarfed/half lap joinery. The shorter the pieces are the less likely it will be noticable that they are straight.
After the joinery is machined lay the pattern on the pieces as they lay to form the curve and draw out the curve. The individual pieces can now be cut close to the line with a band saw or a jig saw. Once the glue up is done, the whole section can be fixed to the pattern and both outside and inside edges can be trimmed to the pattern with a flush trim router bit.
Another method for making the curve is to rip thin strips long enough to make it around the whole outside length of the same type of pattern as above, with enough to end up straight to be joined to whatever is below. For small tight radii, 1/8" will bend easily. For larger curves, 1/4" or thicker may be able to make it without stressing. Do a test piece against the outside of the pattern to see how thick you can go.
Lay waxed paper on the outside edge, and lay the first piece against the waxed paper, and to that one you can clamp up a few at a time. You can use TB III, or if you need more time you can use UF glue (urea formaldehyde) glue, like "Plastic Resin Glue" from Dap. Doing a glue up this way will yield a continuously curved grain pattern. But keep in mind that you can have very tight glue lines and the grain may be defined as to its segments. This works out to be a very predictable lamination with no springback, like steaming or soaking may allow.