How can I trigger a function anytime there is a new session in a GAE/Python Application?
I am trying to be pretty general here as I don't know whether you are using the default users service or not and I don't know how you are uniquely linking your SessionSupplemental entities to users or whether you even have a way to identify users at this point. I am also assuming you are using some version of webapp as that is the standard request handling library on App Engine. Let me know a bit more and I can update the answer to be more specific.

Subclass the default RequestHandler in webapp with a new class (such as MyRequestHandler).
In your subclass override the initialize() method.
In your new initialize() method get the current user from your session system (or the users service or whatever you are using). Test to see if a SessionSupplemental entity already exists for this user and if not create a new one.
For all your other request handlers you now want to subclass MyRequestHandler (instead of the default RequestHandler).
Whenever a request happens webapp will automatically call the initialize() method.
This is going to cost you a read for every request and also a write for every request by a new user. If you use the ndb library (instead of db) then a lot of the requests will just hit memcache instead of the datastore.

Now if you are just starting creating a new AppEngine app I would recommend using the Python27 runtime and webapp2 and trying to leverage as much of the webapp2 Auth module as you can so you don't have to write so much session stuff yourself. Also, ndb can be much nicer than the default db library.
I am a newbie to Google App Engine and Python.
I want to create an entry in a SessionSupplemental table (Kind) anytime a new user accesses the site (regardless of what page they access initially).
How can I do this?
I can imagine that there is a list of standard event triggers in GAE; where would I find these documented?  I can also imagine that there are a lot of system/application attributes; where can I find these documented and how to use them?
Thanks.