When cutting, I like to make sure the scissors are properly held; thumb in the little hole and other fingers in the larger hole and that the scissors and thumb are pointed up. In cutting (and in writing)I often tell the children about their "helper hand". This is the other hand that is not holding the scissors (or pencil). This hand has a job too. This hand has to keep moving along the material that's being cut or it turns the material.
Cutting...it seems so simple but there is a lot to remember when you're little and just starting. But the enjoyment can be in all the interesting things there are to cut. Let's just hope it's not their hair!! EEEEK!