Partial seams, folks. Partial seams. A lot of them. But they're very easy.
Here's a much easier block showing how partial seams are sewn:
http://quilting.about.com/od/piecing...tial_seams.htm
Here's a bigger version of that block in a quilt, also done with partial seams:
http://quilting.about.com/od/piecing...tial_seams.htm
Now go back to the pattern and follow the instructions by number to see how she's slowing building up the quilt.
Also, look at the diagram of the full quilt so you can see how she's starting in the bottom left corner (circled in black).
Yeah, you have to be fairly organized. If you're just doing scraps and a background, it's a little easier. If you're doing a gradiation across the quilt ,then you need to REALLY pay attention, and pretty much have the quilt all laid out before starting.