I use an item I call a stripper. Only can make 1/2", 1", etc but sure helps cut straight.

All the suggestions above are good, but one thing you might want to check is that your fabric is streight before you lay it down to cut. Take the fabric and at the top hold the salvage together, does it fall salvage to salvage all the way down? If not shift it until it does. Yes you will lose some fabric, but at least your cuts will be streight.

There is a clear non skid paper to put on your ruler.

It also makes a difference where you're standing. Position the fabric so you don't have to reach too far across. I like to cut parallel to the edge of the table so I can hold the ruler secure all the way across, walking my hand as others have suggested. Also, while you're paying attention to all these hints, don't forget to watch your fingers. Those rotary cutters are sharp!

On folded fabrics...when you unfold them & they are not a straight line...it's possibably from the fold not being even.

when you fold the fabric (this for multiple folds mostly, not just a single fold)...check each fold...pinch the very edge of the fold...you should not be able to feel the different layers...the fold layers need to be tight against one another..If not...your strips will probably unfold crooked.

When cutting short distances (less than 20 inches, or the length of your ruler), hold your hand with fingers spread out...place your fingers (including your thumb) onto the ruler....if you can, have your pinky off the far end of the ruler (for rulers less than 7 inches wide)..this will help keep it from moving...cut only the amount that is the size that your hand creates...stop, move your hand up...cut again. You don't need to press down super hard, nor do you want to push down super hard with the cutter...If I'm going through multiple layers (I just cut through 8 layers doing strips)..I rock the cutter back and forth a bit as I cut..still just cutting the amount that corresponds to the size of area my hand can reach.

I had that problem until a lady I met at quilts of valor. She uses invisigrip on her rulers and it works great...Good Luck...

Try "painting" the back of the ruler with rubber cement heavily and let dry for a couple of hours. That will keep the ruler from sliding. Or, you can use the sandpaper dots mentioned by the others...but if like me, you're too frugal to buy them, you can just glue some 1" or so squares of sandpaper near the corners of your ruler.

I saw an article with instructions for cutting small pieces of sand paper and using double sided tape. placing them on the underside of the ruler. I couldn't find the 'grip dots', except on the web and I didn't want to wait...
LOL!!! This fixed my roaming ruler problem...

An ergonamic cutter and a slotted ruler for cutting strips and small pieces has helped me.. I must cut sitting and I can't press hard because of arthritus.

Make sure that the table that your using the mat on doesn't have any give. If your using a folding table and put any weight on it, it will 'give'. Then the ruler doesn't meet the fabric and the fabric moves. I don't have a kitchen table so I use my coffee table. I figure if I can sit or stand on it and it doesn't break, it's good to go. LOL