Nothing is guaranteed to keep your communication and browsing completely safe on the internet. But, these programs get you pretty close, and they are free and open source...
The first program is called "Tails" http://tails.boum.org/
Just download the latest version of the .iso file (currently 0.9). You can burn the .iso file to a CD, but I chose to burn it to a flash drive for portability. CD is actually a "bit" more secure.
The second is called "Universal USB Installer" http://www.pendrivelinux.com/downloads/Universal-USB-Installer/Universal-USB-Installer.exe
This will burn the .iso file to a USB flash drive.
The last thing you do is set your computer to boot from a flash drive (if it will, you can usually access the boot menu with F2 or F12 as the computer starts up. then set it to check for a bootable CD or Flash Drive, before it boots from the hard drive.
Plug in the flash drive or insert the cd, then reboot the computer.
What do you get for all this trouble? You will be able to surf the internet, using Tor, through an anonymizing network. If anyone pings your IP address, you might be in Norway or any number of other places. When you are finished surfing and turn off the computer, the memory will be wiped and there will be no trace of where you surfed or what you did. If you are running via cd, and happen to pick up a virus, it will not have access to your drives and will be gone when you reboot. A flash drive is a little more susceptible to virus, since it can be written to. But, just rewrite the flash drive and it will be gone. Because you will operating in Linux, there are far fewer viruses capable of infecting you anyway.
You will also have access to encryption for messaging.
There's a lot more available. But, I am just now getting started with it. So far, it looks very promising. FWIW, I don't do anything illegal. I just don't think anyone else has a right to know what I'm doing and I'm sick of having my surfing habits logged and then getting spammed. Speaking of which, the first thing that I did, when I went anonymous, was to set up a new gmail account that I will never even check to erase. All the spam can go there. I don't go anywhere that I have to log in, anyway, while I'm anonymous.