Paper snowflakes are so easy that I learned to do them as a child. We would start with an 8.5 by 11 inch sheet of paper.
Take a corner and bring it over to the opposite edge, making a square. Cut off the excess strip.
I know this doesn't look square, it's just the way to fold makes the paper sit on the tablecloth. Now,
fold your paper over in half, hot dog style. Next you will fold this in half, hamburger style. See below.
Now you have a smaller square. Next you will fold the square on the folded point in thirds see below. This is folded to the outer edge, but it's popped up.The upper edges should be open edges, no folds.
Now take a peek inside and see the lower edge in there? You will want to cut the top off even with the shortest corners.
Taa daah! Oh, that notebook in the background is hubby's day timer. It's his life, if it ever disappeared he would need therapy. ;-)
Now you decide which edge will be your longer points and start cutting down into the middle of the cone shape, twisted and curving to your heart's content.
Then you start on the other side and work your way down to the small point, but not all the way through.
You should have something that looks like this. Now start on the outside edges and make little nips and cuts here and there if you like. Or you can stop where you are and open. I personally and detail crazy so I keep going.
You can even cut the very tip at the bottom point of your shape.
Now you are ready for the unveiling of your beautiful creation. Isn't this exciting??? I love to see them unfold and open up as a snowflake blooming.
Whaalaa! So now, you may say, hmmmm I want the shorter points even shorter so go back and fold this all up, (good luck) and trim off the tips of the shorter points if you wish. Or, next time, make them short in the first place, ;-).
You can prick a tiny hole and string filament through one point to hang from a window, or tree, or where ever. I usually iron these flat with a dry iron after I'm done making them. Good luck, and have fun!