What I do is tearing the fabric an inch or two from the side. Then I fold the fabric so the selvages are on top of each other and the torn edge is exactly aligned. Then I press a new center fold in the fabric, by going from the selvage to the middle of the fabric, making sure the fabric is lying flat. To make it easier, you can pin along the selvages to make sure the fabric won't shift there. You end up with a new center fold and fabric that's on grain, ready to cut into strips.
I hope that made sense, it's easier to do than explain in words.