Actually it's a little harder still. For instance, when your browser makes requests in your behalf, it provides the destination server with a lot of information which can be used to identify you (at least temporarily)[1]. To get a better level of anonymity, one should at least use a combination of Tor and privoxy [2].
Your information is out of date. The Tor project no longer advises the use of privoxy, and advises all users to use The Tor Browser Bundle. This is specifically configured to make all Tor users look the same, precisely because of browser fingerprinting.
