Since the plastic bag ban was instituted I have been trying various ways of folding newspapers into origami bin liners. To me this seems the easiest and most effective folding I've tried.
Our broadsheets are a different size to US newspapers and for my medium size kitchen bin I actually find laying out 3sheets of The Australian overlapping enough to make a square works well.
https://www.youtube.com/watch?v=b2yfewPAWEg