First, I chose the design. Nice smooth curves, with some intersections for added interest. Using the same technique from the block lotto, I layered my fabrics (5 in this case) and cut all my blocks at the same time. This ensures that the curves are perfect matches for each other. Then, I rotated the colour sets in each pile, to create blocks with different colourways.
Start with fabric squares which are 1-2" larger than you want the finished piece to be, because you are going to lose length and width in your seams, and the amount you lose depends on the sharpness of the curves and the number of seam lines you cut. Also, gentle curves are easier to sew than sharp ones, so keep the curves gradual.
One important thing to remember when piecing curves cut this way - your end points will NOT line up. The seam line on piece on the inside of the curve is shorter than the seam line on the outer piece that it matches. Notice how the orange piece is longer than the black, in this sample. You have to accept this, choose your matching point (I picked the end which will get buried in another seam), and just go with it. In the end, you will trim all the blocks to the same size.
I usually chain piece the same two sections in each block together, then press. Be very careful to keep the pieces in order as you press them. Then when you go back to the sewing table, you simply take the pieces in order off the next pile, and again chain all your blocks.
When you are done, trim your blocks to the planned size (or, figure out the largest square you can get from the completed blocks, and trim all of the blocks to that size, to maximize your quilt).
Here is my finished quilt top, all ready for Hallowe'en. 4 hours start to end, using the curved piecing technique above.