I haven't done a king size yet, but I have done queen size on my small brother machine.
I start by placing the layers out on a bed, attaching the layers with spray adhesive. I neatly fold 5in widths up to the middle from both sides (kind of like rolling, but I fold and smooth as I go). I take it to the machine this way. Now I stitch a straight stitch down the center (I have rolls on either side, so it fits int he throat fine). I repeat this going the other direction. Now I have 4 quadrants. For a larger quilt, I then sew additional lines, say making quadrants in each section following this method.
Now the quilting. When I am working on a quadrant, I have the rest of the quilt in a fold/roll, so it will fit the throat and also so i can easily manuever it.