So, sometimes you want to be anonymous on the open internet for some reason.
Here are a few steps which can help (But may or may not be a perfect way to stay anonymous. Do your own research if you are unfamiliar with this.)

  1. Get a copy of TAILS Linux. (https://tails.boum.org) – TAILS forces you to use the TOR network, keeps no local logs on your activity, among other things
    – Use a VMWare version of TAILS. Revert to new install snapshot every time and don’t save anything from the VM.
  2. Randomize your MAC address with a tool like macchanger or similar. NEVER use your own MAC address, otherwise if your equipment is seized or otherwise found, the real MAC can be left on wireless logs and you’re done. macchanger has a few settings to let you either randomize the MAC or set a specific MAC to something amusing. Just use the random setting otherwise you will stick out in logs somewhere.
  3. Don’t be at the place where you’re using the free wireless network. That means, get a good antenna, be in a car parked some distance away and have tinted windows (Recommended) to avoid being spotted in the area.
  4. Don’t use the same public wireless access point and don’t be predictable online.
  5. Vary your “anonymous” freemail and be vigilant. Otherwise, you’ll be prone to making a mistake and someone will find you.
  6. Don’t talk about whatever it is you do that causes you to want to be anonymous with anyone either in person or online.

That’s about it.
This is just an academic practice for the purpose of understanding internet anonymity.

More here:

http://thehackernews.com/2015/07/anonymity-proxyham.html

BTW TAILS Linux appears to overwrite memory and/or disk data on shutdown to resist hardware forensics. (Researchers have recovered memory remnants from a recently-shut down system using cryogenics.)

Also, study this presentation at DefCon about how people get caught even when using TOR:

Once case he mentions is how to use TOR consistently if you are using a static computer. (e.g., your regular home workstation)
If you browse to a website while on TOR, disconnect from the TOR network and go back to the website; you just divulged your TOR Cookie identity to the web server which can be subpoenaed for prosecution if you are wanted for something.