Weird things happen when I travel. Like, I spend several hours sitting around in airports with nothing to do but write documentation. I am therefore pleased to announce the immediate availability of both upgrade docs and usage docs for the DBTNG system.
If you just want the quick'n'dirty upgrade guide, that's available as part of the Drupal module upgrade guide.
For copious, detailed information about the new API, there's a new handbook section dedicated to it. It doesn't cover conditional clauses (WHERE statements) or Merge queries (highly awesome) yet, but they will soon. Just from the other examples you should be able to pick up the basics of WHERE clauses on Update and Delete statements, which should generally be very simple anyway. Information on writing new database drivers will be included, too, but that's lower priority as there's still a lot of follow-on work to do first.
Webchick has said that now that we have docs, any new patches for Drupal 7 need to use the new API. Help convert core by writing more cool patches to make Drupal 7 even more awesome! And learn the new API in the process.