Chain piecing is one of those easy techniques that can easily speed up your sewing and is a particularly useful trick when you're patchworking lots of straight pieces of fabric together. So to chain piece, you simply sew a seam as usual but at the end of the fabric you pause with the needle down but do not cut the thread. Lift the presser foot up, slide your next piece in and carry on sewing. Keep doing this until you reach the end of the last fabric you want to sew and then cut the thread as usual.
You'll be left with something like this:
Now simply snip the thread between each piece of fabric, being careful not to cut your fabric in the process.
Ta da! Same result as you'd get by individually sewing each seam but faster as you don't pause in between. If you pin a few pieces together before you start sewing, you can sew with very little pause between pieces. Best of all, it uses less thread this way as you don't have those start and end threads to cut off each time.
On both the Silver Star edge strips and particularly on the Lily quilt, this technique speeds up the sewing as long as you're organised so you don't lose track of which piece goes where! I get around this by cutting out every piece of fabric for a quilt or cushion before I start to sew and then I lay it all out on the floor. I then sew in either blocks or rows, split the chains of pieces into their parts again and lay them back on the floor in their correct position. This is easier said than done in our small house though as I sew at the dining table and I have 2 young boys that like to tear around the place! It usually means that I sew while they're asleep or at school and then tidy up before they come home or wake up.