The angles at the centre where the cuts meet should each measure 120 degrees, so cut from the edge in towards the centre for Cut 1. Imagine a right angle to that first line, so that would be 90 degrees...ie you need another 30 degrees to reach 120, so gauge where one third of another 90 degrees would be and make Cut 2 along that line. Cut 3 will just be halfway between the two already made.
Find the diameter of the circle, divide by 2 (or fold in half) to get the radius. From any point on the circumference, step out the radius - it should take 6 steps. Cut from every other mark on the circumference to the centre. Precision - no guesswork or estimation required!