Chain piecing is kind of like sewing parts of your quilt on an assembly-line. After cutting the quilt patches, align them right sides together to prep them for sewing. They'll "stick" together more securely if you place a medium-hot iron on top of each pair, so work on them at the ironing board if you want to take that extra step.
Stack the paired units within easy reach, next to your sewing machine. Start sewing units together, feeding them through the sewing machine one after another, but without breaking the threads after stitching each pair.
When units are all sewn, cut the threads between them and move on to the next step in the quilt pattern.