Start with a square sheet of paper, any size, and a pair of scissors. Fold the paper in half diagonally, so that the lower right corner of the square is touching the upper left corner of the square. Next, fold the triangle you just created in half, so that the far right corner of the triangle is touching the far left corner of the triangle. Fold the triangle a third time so that the far left corner is folded down underneath the base of the triangle. Now the far left corner of the triangle should be close to---but not close enough to touch---the far right corner. Make a final fold so that the right corner of the triangle folds over the seam created when you made the fold in step three. The right and left points of the triangle should be crossing over each other so that they stick out the bottom like tabs.
Finally, cut the tabs of the triangle off with a pair of scissors, creating a new, more narrow triangle. You have now prepared the paper for cutting.
Cut along the edges of the new triangle you created. Cut out any shapes you want---circles, squares, triangles, squiggly lines. The more intricate your cutting, the more interesting the results. When you're done, unfold the triangle to see what you've created. There is no right or wrong way to make a snow flake, but over time you may start to get a sense of what steps you can take to create the shapes you like best.