I took a class on quilt as you go. There are several ways of doing it. I'm not sure I can explain it well, but I'll give it a try for the version I've done.
First, make each block as you normally would.
Second, actually quilt each block with backing and batting. This is pretty easy on a home machine when you're only working with one block at a time.
Third, trim the excess batting and batting from around each block.
Fourth, make the strips that will hold the blocks together. This is done by making two narrow strips. I used a bias tape maker, but it doesn't have to be cut on the bias. Put the two strips of bias tape, right sides together, and sew down the center with a straight stitch, sewing the two strips of fabric together the long way. For example, if you need to put together two 12" blocks, you need two strips of fabric at least 12" long. You can vary the width depending on how much of the blocks you want the strips to cover. Turn them into bias tape (each end folded over to meet in the middle) and sew them together in the middle. When done, you should have one strip of fabric, with a seam up the middle, at least 12" long with four spokes, if you will, coming out of it. Those spokes then get folded over each block, back and front, covering at last 1/4" of the blocks. You then sew the strips to each block, catching front and back with the same stitch, with either a straight or a decorative stitch.
Sew the blocks together in rows, then make longer bias strips to join rows together.
I have no idea if that made sense to anyone but me, but without photos, I did my best!
Good luck!