I started making paper snowflakes pretty much from the moment my parents decided young me could be trusted not to maim herself or her siblings with scissors. There was a dearth of papercutting during my teenage years, but I picked it up again in college. Oh boy did I ever pick it up again. :B
Here's how I do what I do.
Time: Varies Skill: Moderate Caution: This project calls for the use of very sharp knives.
Craft knife (X-acto, etc.) or very sharp, fine-tipped scissors. Craft knives are better, though.
Cutting mat. I find flattened cereal boxes are excellent for this. (Don't use corrugated cardboard as a cutting mat. The knives will just punch right through the top layer into the spaces between, making your cuts too large and destroying any fine details there might be in your design.)