How much a website knows
Assuming you are browsing on a website without any protection, a website can know a great deal of things about a computer. Further, a great deal of this information is generally stored by the website in some sort of database. Often times, websites will store a great deal of information in order to remember some information about you in the event that you log on or register. I would be shocked if a message board did not at least tie your IP to your post in the event they want to ban it if a lot a spam comes from it. Your IP can be traced back to you by an ISP rather easily. It would be rather difficult, however, for CNN to know exactly who you are, though.
How much and ISP knows
Everything not sent encrypted on a network can be logged by an ISP if they wanted. Basically, we allow ISPs to be a man in the middle so we can do the whole internet thing. They basically, then, can know whatever they want about most internet traffic. And they of course know who you are.
What to do
I cannot tell you what the best method is simply because I doubt one exists. This question: http://security.stackexchange.com/questions/13416/whats-the-best-way-to-make-my-internet-traffic-anonymousWhats the best way to make my internet traffic anonymous? has some answers that you may want to look at. I personally prefer HTTPSeverywhere as a method of encrypting traffic to help against normal data interception. This, however, depends on the website being secure itself. Note that proxies and VPNs trade in one level of trust for another. The website will know where the proxy or VPN is located. The proxy or VPN will know where you are located. You are not making yourself impossible to track, just harder. This question: http://security.stackexchange.com/questions/16253/how-does-google-maps-know-where-i-am-when-im-using-a-vpnHow does Google Maps know where I am, when I'm using a VPN? shows some instances where locations services were able to break through VPNs.