I have seen these stars in European Christmas markets. Several years ago, a friend of my grandmother showed me how to make these. With a little patience, you can make these too. I have included plenty of pictures so you can follow step by step.
Step 1: Gathering Matials
All you need is paper cut into strips, and scissors. The width of the paper strip should be no larger than one inch, and no smaller than one cm (otherwise it will be too hard to form the stars). A slightly heavier weight of paper stock works well, but I have made them with good ol' regular paper. The length of the paper is essential. The standard 8.5 by 11 will not do. 11 by 17 will work provided that the width is narrow. Reading on in this instructable, and you'll see why the length is important. The longer, the better.
You can cut your paper into strips using scissors or a slicing paper cutter. If you have a rotary cutter, that works too. Try to be consistent with the width.
Step 2: Step One
You will need four (4) strips of paper. Fold each strip in half.
Step 3: Step Two - Checkerboard Pattern
We will now form the base of the star.
Take one strip and put it between the fold of a second strip. (photo 1 and 2)
Take a third strip and place the folded edge catching the bottom strip in the middle of the fold. (photo 3)
Take the fourth strip and have the strip go over the right top strip (having the fold catch the upper right strip) and through the left folded strip. If done correctly, you should see a checkerboard pattern. (photo 4 and 5)
Step 4: Step Three - Another Checkerboard
Essentially we need to create another checkerboard on top. You'll notice that there's two layers of paper strips. You are only going to use the top layer. Fold the top strip up and over the existing checkerboard. The fourth strip will go over and under to form the pattern. (photo 4 and 5)
Step 5: Step Four - Forming Corner Triangles
We'll be forming small triangle points from each corner on the left side.
Take the topmost left strip and fold behind to the left to form a triangle. (photo 2)
With that same strip fold down so it essentially looks like two triangles. (photo 3). It is a good idea to leave a small gap between the two.
Fold the two triangles together. (photo 4)
Fold the triangle back. We will put the remaining strip through the checkerboard square below the triangle we just formed. (photo 5 and 6)
Slide the strip through the square below the triangle. Once through, the strip will lay on top of the checkerboard. (photo 7 and 8)
Turn the star and REPEAT the process THREE MORE TIMES. Remember to use the left side only. If done correctly it should resemble photo 15.
Step 6: Step Five - Forming Second Set of Triangles
Flip over the entire unit and repeat Step Four. Essentially you are creating another set of triangles, on the left side. Once you finish all four on this side it should resemble Photo 6.
Step 7: Step Six - Forming Cone Points
This part can be a little tricky. To start, fold back each strip to form a crease. To form the cones, fold back the strip beside the one you will be working with and curl the next to the right. (photo 3)
On the curled side, take the strip and slide it under the folded back strip. Pull tightly. (photo 4 and 5) If your cone is not pointing upright, you curled in the wrong direction.
The remainder of the strip will come out between the triangles you formed in the previous step. Form cones three more times so you have 4 cones and resembles photo 15 and 16. If you have trouble sliding the strip through, you can fold the corner over to form a point as in photo 8 and 9.
Once you have finish, flip over and repeat on the other side. (photo 17)
Step 8: Step Seven - Cut Strips Off
Cut the strips off at the triangles. Congratulations, you have made a star! You can leave it as is or spray paint it for added decor.