This is where your imagination comes in. Begin cutting away from the sides of the paper. Usually, cutting small triangles from the sides is easiest, but don't forget to try other shapes.
For this snowflake, I altered the top edge a little to make my points a different shape. I also cut out a piece with a "spiky" edge. Use your imagination!
I don't use patterns for my snowflakes: I just cut as I go. My snowflakes are never the same because I don't usually plan out my snowflakes. Sometimes I find a new cut or shape that I like, and I may use the same technique on a different snowflake, but I don't copy the whole snowflake.