Originally Posted by feline fanatic
I was taught a quick method to straighten grain. Simply pull on the bias of the fabric from one corner to the other. Do it both ways. Then when folding to cut you can see the "drape" if it was not cut straight. Then, with selvedges matched I move one cut end over until the fabric hangs straight when folded. This keeps my cut strips nice and straight with no dog legs. I was never taught the pull a thread method but it does sound like it could come in handy on some fabrics where you really need the straight of grain.
I have done both. Sometimes I do the corner stretching bit if the fabric looks really wonky. I do it when I am ironing it. It is very important in apparel and home dec sewing to find the true straight of grain or your clothes or drapes won't hang straight, but not so important in quilting since you are usually dealing with short pieces of fabric and cross grains. Most of our quilting fabrics have printed designs rather than woven designs so the straight grain doesn't really matter.