1. Get yourself a blank cd/dvd or USB flashdrive.
2. Go to The Downloads Page and download the disk image.
3. Burn said ISO to disk or to the USB drive (Google will explain how to do this)
4. Insert disk or USB into the computer and boot.
5. Boot the Linux Mint Live Session
6. Ensure you have an Internet Connection
7. Double-click "Install Linux Mint"
8. Follow the detailed directions of the Linux Mint Installer.

If at any point, you have trouble, You can refer to the Linux Mint Installation Guide which is fair more detailed than I have been.

One of the things about Linux that some people struggle with is that it is not a "hold your hand" kind of OS. If you have trouble, you are expected to do a little bit of googling and/or troubleshooting yourself. So definitely get in the habit of reading the manual.

Linux Mint was definitely a good choice for a 'first step'. It is very user-friendly and I believe designed to appeal to people coming from Windows with no experience with Linux in general.

Thank you! Great info. I have ran into a slight problem. It's been almost 10 years since I have been able to use this laptop. I have forgotten/misplaced the administrator password to be able to boot Linux Mint. I have the service tag for the machine as well as the product key for the version of Windows XP Media Center Edition 2005 that was originally installed. I had someone years ago install Linux Ubuntu on it, so I am now upgrading from Ubuntu to Mint, attempting to do it myself. Is there any way I can get around having to insert the administrator password or even edit it?

I'm going to assume you are referring to the BIOS administrator password? I'm not 100% sure about how to get around that, I've never bothered with it myself.

This Article seems to offer a solution, but i do not know if it'll work for you. Worth a shot though.