None at all really, as long as you can use a PC/Laptop you should be able to download and try Linux. Personally I would recomend going for an easy to install distribution first. When I started with Linux I first tried Ubuntu and had no problems at all.
If you want to replace your desktop environment with a desktop environment based on *nix, then you should probably start with Ubuntu, Fedora or CentOS (just to name a few of the easer desktop oriented ones).
You should probably start by running the OS in a VM (which is a virtual computer that you can run without deleting your old OS) first. VMWare Player works quite well. Another popular option is VirtualBox.
If you want to learn more about the internals of *nix, then you have a few options. If your running Windows, you can install Cygwin which will give you a Linux like environment to work with (enough to understand the system). If you would prefer a whole OS, then Arch Linux (a minimal "build-it-yourself" linux), FreeBSD and Minix 3 (this one is designed for education. It's easy to look at and modify the source code, and it is a fairly simple system to understand). Again, I would start by running these in VM's. Also, learn how to use man and info. You'll find most of the usefull documentation there.