I'm now sold on the method, but will not claim it is the "best" method, that will be up to your evaluation. However, it is a method you should consider, along with water stones, ceramic stones, oil stones, and diamond stones.
Step 1: Why sandpaper?
One excellent method using water stones is already published in Instructables: http://www.instructables.com/id/Tool-Tip-How-to-Sharpen-a-Chisel/
So why consider another method, and why would you consider using a piece of crude sandpaper on your precious woodworking chisels and plane iron?
Here is the main reason: cost. Cost of good water stones is $100 and up each (you should have several of various grits). And sandpaper? Less than $2 per sheet. This is not a fair comparison, however. A water stone will last years; you will have to buy many pieces of sandpaper and replace as they wear out. But bottom line is that the sandpaper method is a lot cheaper.
Second reason: Simplicity. The sandpaper method is pretty easy.
Third reason: For most of us the sandpaper method, if done carefully, will produce the sharpest cutting edges we have ever experienced.