Ubuntu is a Linux distribution. Ubuntu is considered the most user-friendly distribution of Linux, and so it's the easiest to use while trying out Linux.
How do I Install?
Following these steps should get you through the installation nice and smooth:
Get the Ubuntu ISO file at Ubuntu's Official Site http://www.ubuntu.com/getubuntu/download.
Alternatively, you could buy or request a CD with Ubuntu already burned into it, but buying costs money and requesting takes awhile.
Downloading will take awhile, as the file itself is over 600MB.
Burn the CD Image
An ISO file is the type of file that is usually burned to a CD or DVD for later use. You can use Nero or other Disc burning programs for Ubuntu.
Alternatively, you could use VMWare to make a Virtual Machine within your own.
Load Ubuntu
Once Ubuntu is loaded, you may start the actual installation:

Open the "Install" icon on the desktop. This will take you through the extremely simple installation wizard.

Select the language you want to use and continue.

Choose which time zone you live in.

Click on the keyboard layout you wish to use.

Now here's where it might seem tricky. At this point, it'll ask you how you'd like to partition your drive. Since the scope of the tutorial is mainly installing on a clean disc, stick with "Guided". As you can see, I'm using a 2GB "disc" made in VMWare.
WARNING: Do not install on your computer if you already have an operating system, as you will definitely lose all of your data! This tutorial only deals with installing on a computer that hasn't already had an operating system installed.

Fill out your name, and choose a good password.

Now confirm your installation settings, and change things where required.

Wait until it finishes installing (may take an hour or 2), then reboot.
Congratulations!
You've successfully installed Ubuntu Linux!
What Are the Advantages of Ubuntu?
It's a free, easy-to-use operating system that's being used more and more by people who want a more stable and secure operating system. It has many of the same capabilities, as well as many features not available in Windows.
Have fun using Ubuntu!
I ended up using "PCLinuxOS", another 'easy-use' Linux Distro. PCLinuxOS is about as easy to use, maybe a few things not quite up to Ubuntu, but it too is a great distro for anyone wishing to wean themselves from the chokehold grip that Windows-whatever has on their computer.
I still recommend Ubuntu favorably for security & ease-of-use. :)