Start with an 8.5" x 11" sheet of paper. Fold one corner of the piece of paper down. Cut off the bottom portion to make a triangle.
Temporarily bring the two corners of the base of the triangle together to find the center point of the longest side. Make a small crease at the center point.
We're now going to use the center point identified in Step 2 to divide the triangle into three equal parts. Fold the right corner in at a 60° angle. (Use a protractor to help you.) Then fold the left corner in back at a 60° angle.
Your paper should look like the illustration at right. Now fold the paper in half as shown.
Cut off the upper portion along the horizontal line.
This triangle will be 1/12th of your snowflake. Use a pencil to draw a design on the triangle. The unopened side will be the backbone of the snowflake. Do not draw any lines that cut through the triangle.
Use a pair of scissors to carefully cut away the unwanted area.
Carefully unfold your snowflake and flatten it out with your fingers. Voilà!
Now experiment with different designs and see what you come up with. One of the joys of cutting paper snowflakes is that you never know for sure what the snowflake will look like when you open it up!
If you'd like to see some example snowflakes, you're welcome to view my snowflakes collection on flickr. You might also be interested in the flickr group Paper Snowflakes.