For IBQLTN:
I found the method somewhere online, but can't find my bookmark right now. I cut the backing 1/2 to 3/4-inch larger all around the block. I quilted the blocks and stopped 1/2-inch from the edges all around. When I was ready to put the blocks together, I pinned back the backing and batting, matched up the fronts and sewed them together, using a 1/4-inch seam. I trimmed the batting to butt up and not overlap. I trimmed one side of the backing to overlap the seam by 1/4-inch and pressed the other under 1/4-inch to overlap the backing I trimmed. I then hand-stitched the backing down. When I had joined the blocks into a row, I went back and finished quilting the blocks to the edges.
On my niece's quilt, I machine sewed through from back to front because I didn't want to hand-stitch. It looked just as good.
Hope that helps.