I want to use a Python framework that handles sessions (user auth), templating along with MySQL database access (although I can use MySQLdb quite nicely)
Tornado looks promising but, I just can't see how to use it. The sample given has a port listen feature. Does it replace Apache? Exactly how do I configure my server (Centos 5.4) and LAMP setup for this, or is there a better option?
Use Django. 
I'm a hardcore Tornado fan but if you need to ask, Django is the best tool for you. Tornado is great but Django is much easier to build when you need a MySQL database thanks to its awesome ORM.
python tornado setup