You can place your fabric on the die any way you want, but normally you would want it parallel to the blade regardless of how it sits on the die.
You want to feed the blade into the die at an angle so the blades on the larger dies are set at and angle already. Usually the smaller dies are set with the blades parallel with the die block. You should feed these into the roller at a slight angle, but watch that you don't hit the sides of the roller housing.