standard way to handle user session in tornado
Here's how it seems other micro frameworks handle sessions (CherryPy, Flask for example):

Create a table holding session_id and whatever other fields you'll want to track on a per session basis. Some frameworks will allow you to just store this info in a file on a per user basis, or will just store things directly in memory. If your application is small enough, you may consider those options as well, but a database should be simpler to implement on your own.
When a request is received (RequestHandler initialize() function I think?) and there is no session_id cookie, set a secure session-id using a random generator. I don't have much experience with Tornado, but it looks like setting a secure cookie should be useful for this. Store that session_id and associated info in your session table. Note that EVERY user will have a session, even those not logged in. When a user logs in, you'll want to attach their status as logged in (and their username/user_id, etc) to their session.
In your RequestHandler initialize function, if there is a session_id cookie, read in what ever session info you need from the DB and perhaps create your own Session object to populate and store as a member variable of that request handler.

Keep in mind sessions should expire after a certain amount of inactivity, so you'll want to check for that as well. If you want a "remember me" type log in situation, you'll have to use a secure cookie to signal that (read up on this at OWASP to make sure it's as secure as possible, thought again it looks like Tornado's secure_cookie might help with that), and upon receiving a timed out session you can re-authenticate a new user by creating a new session and transferring whatever associated info into it from the old one.
So, in order to avoid the "no one best answer" problem, I'm going to ask, not for the best way, but the standard or most common way to handle sessions when using the Tornado framework.  That is, if we're not using 3rd party authentication (OAuth, etc.), but rather we have want to have our own Users table with secure cookies in the browser but most of the session info stored on the server, what is the most common way of doing this?  I have seen some people using Redis, some people using their normal database (MySQL or Postgres or whatever), some people using memcached.
The application I'm working on won't have millions of users at a time, or probably even thousands.  It will need to eventually get some moderately complex authorization scheme, though.  What I'm looking for is to make sure we don't do something "weird" that goes down a different path than the general Tornado community, since authentication and authorization, while it is something we need, isn't something that is at the core of our product and so isn't where we should be differentiating ourselves.  So, we're looking for what most people (who use Tornado) are doing in this respect, hence I think it's a question with (in theory) an objectively true answer.
The ideal answer would point to example code, of course.