To begin the next section you can either continue on using the same string if it's long enough. Or you can start with a new string. If you start with a new string, simply thread it through one of the perimeter pieces and tie the end to the existing string to secure it. Then you will thread 3 straws onto your string and thread your string back through the first straw in this series of 3 (first image below).
From here you will just continue on as you did above and thread 2 straws, loop it through, thread 2 more and so on and so forth until you finish your next shape (second image below). Then start the next section just as you did this second section.
When you get to your last shape, you will begin in the same manner I described in the previous step, loop 3 straws in the same manner, then instead of threading 2 straws and continuing on, you will simply thread through the perimeter piece on the adjoing shape (third image below). Those 2 points are the only points in which your last shape will connect to the existing shapes. Then you will simply continue on forming your shape.