Search and you will find lots of ideas, suggestions, photos, tutorials.
Here is my approach:
I quilted this improv Logcabin in three rows.
I stopped quilting about two inches from each side.
{But you could quilt all the way to the edge on one side: the "bottom' side.*}
Then, layer the two rows.
On the bottom row, all three layers of the quilt sandwich stay intact. On the top row, turn back the batting and backing, then stitch the top to the bottom row's three layers.
Next, trim away the excess batting and backing from row one.
[* Note: if you stitched all the way to the edge on row 1, the excess should be trimmed away before attaching row two.]
Spread the two rows flat, and trim the excess batting of row 2, so that the batting butts against the row 1 batting.
Fold under the excessive backing so that the edge overlaps the seam line where row 1+2 joined, I secured the loose edge with a small strip of fusible [MistyFuse@ is my prefered brand].
Turn the quilt back over and quilt the unquilted areas.
The back looks great!
Repeat this process as many times as needed.
My finished blocks were 16.5 inches. No trouble under the machine!
Links to other QAYG pages:
http://pinterest.com/pin/219198706835987463/
http://lilysquilts.blogspot.com/2011/04/quilt-as-you-go-joining-blocks.html
http://www.thequiltingedge.com/p/tutorials.html
...there are many, many more!
