I learned how to cut linen properly last week, when I was wrestling with a very large piece of fabric for this DIY headboard project. Linen is a wily fabric and its loose weave likes to change shape a lot when handled. No matter what I did to line it up, the linen would shift and I couldn't cut a straight line to save my life. Thank the heavens for this amazing tip:
Here's the fabric I used. You can see here how it "bends" and makes finding a true straight line difficult.
First, pick out a single thread on the frayed edge (not selvage) of the fabric, in line with the cut you'd like to make. Once you isolate one of the suckers, give it gentle but firm tug. As you pull, the linen will bunch up a bit, creating a ruching effect.
Eventually the thread will snap, but look! It leaves a telltale sign where it was before. Cut along that mark and you'll get a straight line.
When you get to the place where your initial thread snapped, choose another thread in the same line (in the "V" of your cut), and repeat the process until you get all the way to the other side.
It's like runway lights guiding you home, but in this case the airplane is a pair of scissors and you're not so much a pilot but an upholstery god(dess).