My basic question is how to go about this.
If you want to have an intensive discussion with someone over this, through the internet: For communication that may happen burst-by-burst, leading to something definite later, google wave is an idea.
For a collaborative effort allowing anyone to contribute: Since you might perhaps want anyone to be able to contribute, starting a wiki is a good option. There are many sites allowing you to create wikis for free. Adding latex support also will be quite easy. If you want a ready-made place listing tricks, methods and their usage, maybe you can create a few pages at Tim Gowers' site "tricki" for various excerpts from Vinogradov's book.