The rules of cutting a snowflake are simple. If you start cutting from the left side, end on the left side. If you start on the right, end on the right. The only times you will want to cut from one side to the other will be across the top, which will become the outer edge of your snowflake, and you can also cut across the very bottom (but don't have to), which will become the center. Gripping the layers together tightly will help with the more intricate designs.
Here are a few patterns to get you started. Once you get the hang of it, try cutting out a few random shapes, following those rules, and you will be surprised at the lovely snowflakes you can create on your own.
Use a hole punch to create the circles picture below. It is a pretty effect, but a pain in the... hand. Lift one side and punch through that layer first, then repeat on the center and other side. (You can use the holes punched on the first side as a guide to keep everything lined up.)
And, if you ever see a see a flake that you really love and want to re-create on your own, it is easy to make a pattern. Take the photo and draw six lines across the snowflake, along the lines of symmetry. Any one of the twelve sections will work as a pattern. (This photo is used for the first pattern above)
You can also enjoy a little virtual cutting on this fun site. If your finished flake turns out really lovely, click 'cut some more' to go back and you will already have a pattern to cut out the flake in real life.
I hope this all helps de-mystify things a bit. Have fun creating your own flakes and be sure to post them for us all to see. Happy cutting!