It's subtle. The second phrasing ("how not to x") is idiomatic, and means, roughly, "some things that you should not do when you do x", or "an example of how yo

It's subtle. The second phrasing ("how not to x") is idiomatic, and means, roughly, "some things that you should not do when you do x", or "an example of how you should not go about doing x." So, an article titled, say, "how not to paint your house" would be expected to outline things to avoid when painting your house, and "how to not paint your house" could just be "go for a bike ride instead."