Piecing goes a lot quicker if you "chain piece" and start with a "lead fabric".
A lead fabric is just a scrap that you run through the machine before you put your actual project in it. It catches the messy ends of the thread and also lets you know that the machine is working correctly before you stick your beloved project in it.
To chain piece first sew across your lead fabric. Don't pick up your foot or cut your thread once you're done; simply sew your next piece immediately afterwards. Do the same with all your pieces, one after another, being careful not to actually sew them together but leave a few chain stitches in between.
When you're done with your "chain" all of your pieces will be strung together. To me, when they're in this state, they look like those Tibetan prayer flags people hang in front of their houses.
Snip the thread between them and iron as usual.