I use a color-blending technique. In my opinion the quilt squares should be the focal points of the quilt. The sashing and borders should be in a subtle but elegant supporting role.
First, I always cut more sashing and border squares than is actually called for in the pattern instructions. I cut my squares from a wide range of colors used in the quilt block and anything else that I can lay my hands on that will blend into the palette. The fabrics can be actual leaf prints, but it is the character and color of the the fabrics that is most important. I look for an organic, natural, "Mother Earth" flavor. I include the full value range of lights, mediums, and darks in my color selection. The only exception would be fabrics that are lighter than or virtually the same value as the background fabric of my quilt blocks. But just one step above that background value stays in the mix.
I arrange the quilt blocks on my design wall according to my pattern. You may, of course, choose to arrange them as you wish. I decide then on where I would like to accentuate the light areas and the dark areas. On the smaller quilts I like to have two light corners diagonally opposing and two dark corners diagonally opposing. On the larger quilts, I will also begin that way, but there are lots of opportunities to play with the values across the intersecting lines of the design. I put my 2 1/2" sashing squares all over my design wall very near the quilt so that all the choices are at my fingertips. Then I start in one corner, for example, with the lightest light, and work my way down the line to the darkest dark on the next corner, gradually changing value and color as I go. Right or wrong, at this point it doesn't matter. I just want to get squares up there to begin with. I wouldn't start with yellow and then try to get purples in next. I would move from yellows, to oranges, to reds, to browns, to greens, and then purples would blend in that area. I also overlap the squares by 1/2" so that I can fit in the correct number that the design calls for.
Then, step away from the design wall (5, 10, 15 or more feet) and see what it looks like. I am attempting to create a blending of color rippling through from shade to shade and value to value. The size of the quilt and how many squares of each color run together determines how many values I can put in the color run. Three browns in a color run would probably all land in a darker value area, but if there were eight or nine browns in a run I could use lights, mediums, and darks. If the brown area begins at the end of a dark red area I could start off with my dark browns, then work in the mediums and finally the light browns. Next could be lighter greens and so on. By stepping back from the design wall I can easily see where colors or value have been misplaced. It always looks different from further away. Some squares may need to be replaced but others may simply need to be rotated, such as batik fabrics that have more than one color in each square. Turning them another way can help them blend better.
It is tempting to strip-piece fabrics for the sashing and border squares. I do not recommend it because it does limit the options for arranging the colors and values to their best advantage.
I also find it helpful to have whatever I feel is the final layout up on the design wall for a few days. I continue to look at it at different times during the day to see how the changing light effects it. Usually I will find a few more changes to make. After the quilting and binding are complete I may still find a questionable square here or there. At that point I just call them "flickers of interest" and leave it at that!