I don't have a Sizzix, but I assume it works in a similar way to the Accuquilt Go! that I have. I simply take the fabric fold as it came off the bolt and use that. I have marked lines on my die that run perpendicular to the die blades, and place the fabric fold along one of those marked lines near the end of the die. This gives full-width (42-44") cut strips.
I precut the fabric length so it is just a little wider than the die (1/2" to 1" wider).
When rolling the fabric and die through, I find that I need to stop at least once midway to lift up the mat and pull the fabric straight. This is because the roller is pushing against the crossgrain, which is stretchier than the lengthwise grain. Sometimes I make two stops to do this. Otherwise I end up with creases in the strips that I need to iron out (the "waves").
With my Go!, I can cut 4 layers at a time with the strip cutter (2 strips of fabric at a time, since the fabric is folded).