Hey - sounds like a fun project, for you and your nephew
Getting started with Linux is easier than you might expect. The first thing you'll need to do is get a copy of whatever version (we call them 'distributions') of Linux you want to run. Don't think too hard about this, there's really not so much between them these days. Best to start off with Ubuntu, Linux Mint or Fedora, I would think.
How do you get a copy? Visit their websites, where you'll be able to download an 'iso' image. It will be quite big, in the region of 700Mb, so you'll need a decent internet connection. Once it's downloaded, you'll need to burn it to a CD. On Windows, a program like http://isorecorder.alexfeinman.com/isorecorder.htm
will do the trick. Note that you can't just burn the iso image like you would a picture or audio file, it's a special kind of file that must be burned properly.
If you don't have a fast connection, try and pick up a copy of Linux Format - we always have several distributions on our cover discs.
Once you've got a disc, pop it in the disc drive of the computer you want to install Linux on, and then start it up. When the Dell logo appears, you'll need to press a key to tell it to start from the CD rather than the hard drive. It varies from computer to computer, but usually it's F2, F12 or Del. One of them should cause a menu to be displayed, from which you can select the CD drive.
After that, sit back and wait for it to start. What you'll be running is a 'live CD' - it will let you try out the entire operating system without even installing it. It will run a bit slower than a real installation, but it's more than fast enough to explore and check everything works properly.
If you decide you like it, have a look around for an 'Install to hard drive' option or analogous, and you'll find that installation is quite simple and fast. After that, reboot, taking out the disc, and then your computer will start up in Linux with a whole new world for you to explore.
If you have any problems (some bits of hardware can be tricky to get working, particularly the advanced abilities of graphics cards, and WiFi) drop by here and ask for more help and I'm sure someone will be able to help.
Good luck on your new adventure