I make waldorf star lanterns for years, but start differently to the ones I have seen on some blogs. Here is my short description with pictures, in case you don't find way through you can email me your question and I will try to explain more.
As said, I do not start with circular paper, I start with a square one, approximately 25x25 cm. I use wax crayons and paint one side.
I oil the paper after folding (unfold, oil and fold again). This is needed to do so the light shines through the paper.
I make each fold both ways to make the final folding easier.
I fold the square in half and half (to get quartes) and again in half (to get eights), and once again in half, so I get sixteenths:
(here is a hint how to fold for the last time)
then I cut four (in the above picture white) triangles away
and then I start folding this way:
so that a new square appears. I unfold, rotate the paper for 45 degrees and fold the same way again.
then the folding becomes a little tricky:
I fold the top edges of one "kite" shape inwards, around and around, so I get eight "kites"
I made the little triangle in the bottom of the "kite" as a help to unfold. It will become the bottom of the lantern, place where the candle will be.
Start folding the little triangles on the top of the kites (around and around)
and then it is time to make the bottom flat.
I like to make the top edges sharp, the lantern looks more beautiful to me.
I hope you can understand my tutorial. Email me in case you do not.