Video of it in action at: http://www.youtube.com/watch?v=xKQ3d_iASho
Step 1: Materials
You'll need 6 pieces of paper, square if you have it. Start with plain old white printer paper and after you have the hang of it, feel free to get creative with shiny pretty coloured papers.
Scissors, and tape or a stapler is all else that is needed.
Optionally for hanging it you can use a hole punch and some yard or string.
Step 2: Square the Paper
Once you do this for one, you'll have your square so you can either use that as a guide and cut the remaining stack of five, or if you want to be extra precise, do the fold and cut for each other piece.
If you already have fancy square papers (or not so fancy... have you tried newspaper for a really large one?) around the house, you can skip this step.
Step 3: Fold the Paper
Just fold the square into a triangle by taking one corner and folding it down to it's opposite corner.
Then repeat this again so you have two folds (4 layers).
Now do this for each of the 6 pieces.
Step 4: Making the Cuts
You want to orient the paper so you have the side with the fold on it. You'll be cutting from this edge of the triangle, parallel to the long edge of the triangle.
Find the middle of this edge, and cut from there until you're 2cm away from the other short edge of the triangle.
From the middle cut, find the middle again between the cut and the corner to the left, and cut again until you're 2cm away from the other edge.
From the middle cut, find the middle again between the cut and the corner to the right, and cut again until you're 2cm away from the other edge.
Double check the photos before you cut so you're going from the correct edge, in the right direction. It's a bit unusual for most as they want to cut perpendicular to the edge you're starting the cut from, instead of parallel to the long edge.
Step 5: Unfold and Confirm You Have the Correct Cuts
If so, flip it over so that the main 'valley' fold is a 'mountain' fold.
If you didn't make any mistakes with this one -- repeat the fold and cuts for the other 5 squared off sheets of paper before continuing to the next step.
Step 6: Rolling It Up
Now flip it over, and do the same thing with the next pair of flaps out from there (except they'll be bigger so you don't need to roll it around your finger). If you're using a heavier paper you might find you need to use a stapler here instead of tape. Your mileage may vary.
Flip it over again, etc until all pairs of flaps are connected up and you have one of the 6 units of the final snowflake star.
You'll probably want to follow along with the photos on this step the first time through.
Step 7: Connecting the Pieces
Start with your first pair. Make sure they are facing the same way, in that the most outside roll is to your left for each. Then connect the one of your right (the most outside bit) to the one on the left (its 2nd most outside roll) right in the centre part.
Then connect the ends closest to you together, letting them bunch up a bit while doing so.
Do this for the 3 pairs.
Step 8: Final Assembly
To finish up, attach the third pair, back to the first pair.
Step 9: Hanging
You can just tape a piece of yarn to one, and hang it from the ceiling (if you're fancy and do it near a light it'll probably move do to the air currents from the heat of the light).
Another option is to use a hole punch, and loop string through it and hang it from a curtain rod so it's hung in the window.
Enjoy! Feel free to post photos of the ones your make with your family.