Check out the tutes on the Missouri Star Quilt Co. website. That is where I learned to cut with a rotary cutter/

Others probably have a better understanding of this than I do, so, Others, please feel free to chime in. If your fabric isn't folded with the straight of the grain, you can get a "bend" where the fold is. It isn't always straight just coming off the bolt, even though it's got a fold line. You might check that.

Another thing you might check is the nut that holds the blade in your cutter. If it's too tight or too loose, your cuts can get wonky. When I change a blade I tighten the nut fairly tight & then back if off a little. And be sure to remove the blade periodically & clean out the lint.

Stick some non - sliding dots or dots of sandpaper on the underside of your rule. Make sure your blade is sharp. Don't try to cut through too many layers at once. Put even pressure with the fingertips of your hand pushing down in centre of the rule. Don't lay your hand flatly on the rule. Hope this works for you. If you need more assistance, you can buy a suction cup that is like a door handle, to put onto your rule and press down on that.
One other lady showed, in a recent post, how she uses clamps to hold the rule down.

You can also buy the gripper handles at Harbor Freight and Walgreen's for about $3.

I have tried the plastic dots and I didn't like them, just my opinion. I will try the sandpaper dots as so many have great things to say about them.

I have a ruler that has a "lip" on the end which attaches to my cutting board. It is great! Got it at Hancock Fabric.

I find cutting single layers more accurate than multiple ones. I prefer to cut with a 45 mm blade. I cut curves with a 28 or 18 mm blade.

If the table you are bearing down on has any give to it at all, it will affect your cuts.

Sorry if somebody else already offered this tidbit....I haven't read them all.

Another tip is to make sure your fabrics are starched well. It helps with the distortion.