Lots of things to suggest...
Prewash your fabric then really give it a heavy starch. Stiff fabric is much easier to cut straight.
Get a good quilting ruler. Being able to see what you are doing is important.
Keep your fingers out of the way.
It should not take a lot of pressure to cut fabric.
Cut only one layer at a time to start. Measure very carefully.
Use good fabric. Cheap fabric unravels.
We all were (are?) beginners at some time. I never touched a sewing machine till about two years ago. three complete quilts and three more tops later... voilla!
tim in san jose