Ubuntu is the easiest to get in to that I have tried. Also it seems to be the best os for steam from what I have heard though things might have changed.
All of the Linux Distros are free. I've tried Ubuntu and Fedora, but there are many more. Do some research and determine the best fit for you.
The installation process will be very similar. You need to create a bootable USB stick/CD with the OS .iso file. If you don't have a CD/DVD drive you can create a bootable USB stick using Rufus: http://rufus.akeo.ie/