I agree with prism99. The folded edge is the key. I have to fold at least twice to make 4 thicknesses because of lack of space. I put the folded edge on a straight line on my mat. Then, using a 6" wide ruler, place a line going across the ruler on the folded edge/mat line, and cut on the long edge of the ruler. Move the ruler over counting squares on the mat, line up the width lines, and cut against the long edge. I saw this on simply quilts. Basically, you move the ruler, not the fabric. I, too, make sure the folded edge is toward me.
I never iron first. I smooth with my hands. I'm lazy. 8)