180 Days of Ideas for Discussion in Math Class.
(as of 9July2014, we're in overtime!)
The best way to do division is whichever way you personally like best. But the best way to teach it would probably be the scaffold. It makes sense more easily than the standard algorithm, and it's easier to do than the efficient version. Students will evolve toward the efficient method if they do division by hand often.
I have shown this to adults who weren't comfortable with division, and they have been excited to understand the process. (The conventional method hides the reasoning too much.)
Where Did You Get 360 To Subtract From??