All you will need for this is paper and scissors. Some people like to use fancy paper, but I use plain white copy paper because somehow the simplicity of white is more beautiful to me.
If you want to view a gallery of my snowflakes, see me on Flickr: Paper Snowflake Gallery.
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Step 1: Step 1
You can make a square from a rectangular piece of paper simply by folding one corner down to form an isosceles triangle (like the one in the next step) and trimming off the excess paper.
Step 4: Step 4
See the explanation above, from a worksheet I made up, which should help to explain folding in thirds a little better.