How to cut fabric straight?

[mari123]

Well, the plan for table decorations was to make some placemats in my wedding colours, just by cutting rectangles out of fabric, since they only need to last a few hours. Fairly simple I thought.
So, out I went and purchased a few metres of a nice chiffon fabric. I also bought a pair of pinking shears as I thought I could use those to make the edges nice.

I tried to get started last night though, and OMG it is so difficult! I just cant seem to cut in a straight line, either with normal scissors or with the pinking shears. I think the main problem is that the fabric is so light and flimsy, so it shifts around too much.

I tried using a heavy book and tracing an outline of it, then trying to cut to that. I can cut along the line just fine, but then I find that the line isn't straight! Because the fabric shifts underneath when I am drawing the outline.

So anyway, does anyone have any tips that could help me cut this stuff straight?