Now, this may not be the best or easiest way to piece a backing: it's just the way I do it. The first thing is to pull fabrics. I generally try to find fabrics that sort of coordinate with the front. I don't want too many of the exact same fabrics or colors since I like the interest of a mix of colors. When I say "sort of coordinate" with the front, I like a bit of difference so that there's something interesting and different on the reverse.
Once I've chosen the fabrics, I begin by trying to determine a common size among them. In the fabrics that I pulled for this quilt, I noticed that I had several fat quarters, so I cut a few more from the yardage that I'd pulled.
I had several small squares and two leftover blocks. These I sewed together to create a large section. I found it easiest to sew the smallest pieces into one section, the larger pieces into a different section, and then the odd pieces into a third section. (See photo below.)
The next step is to work with the fat quarters. Working with fat quarters is relatively easy because they are 18" x 20", so it's important to match pieces to that size. I square up the pieces by laying out a stack of four or five. Trim one edge, then use this straight edge to square up the other edges. Once they are all square, I sew them together by matching the same size edges. As I sew, I try to keep the new pieces close to the same length so that they go together easily. See the fat quarter rows in the picture below.
Now that I have several large sections, I start figuring out how they go together. The design board makes a fabulous assistant for this part. In this case the odd pieces section and the small pieces section fit together nicely. After they were sewn, I squared up the edges of the one large piece.
The next part of the backing that fit together were a fat quarter row and the large pieces section. Again, I squared up the large piece after sewing.
I added the long single piece to this section so it would be the same width as the first large piece on the top of the backing and sewed those two together.
I added some smaller pieces to the long fat quarter section because I needed more length. I measured several time to double check that I had the right length and then sewed the fat quarter section to complete the backing. The quilt top is 101" square but the backing needed to be 105" or larger. Somehow I managed to get 107" so I didn't worry about squaring it up. I'll do that after I've quilted it all.