Ricky Tims says to only use your mat to line up your fabric and to use your ruler to measure and cut from the left to the right....but that's Ricky Tims. I've seen him "cheat" already though, in his flying geese tute on YouTube. Imagine that! LOL
My personal experience...I started out using my mat to measure and cut from right to left with a good measure of success. Over time though, grooves were worn in my mat, aging it well before its time. I've switched from doing it that way, to using the mat to line up my fabric and using my ruler to cut from left to right. I've found by doing it this way, my strips were more accurate. It is a pain to have to use 2 rulers when your strips measure more than 6.5 inches, but to me, accuracy is worth more than ease...but that's just me. Experiment and see which one works better for you. Rest assured that whichever method you choose to use, it will not prompt a visit from the "Quilt Police". I've tried a bunch of things that were suggested on this board that I might not have tried before...some worked, some didn't, but at least I gave it a shot. Quilting is all about enjoyment...if you have to apply rules, it becomes a chore. So use what works for you and have yourself a great time doing it!