Take a computer, download the ISO(s) for the distro that looks interesting to you ( you can download them from
DistroWatch or
LinuxISO), and install. Installation guides are usually provided at the website the distro originates from and I would suggest following that.
As far as learning linux, it involves way more than I could begin to explain here. A Google search will provide you with more information than you'll know what to do with and I would start there along with linux support forums. It's going to take some time and commitment on your part, but after learning the basics, I think you'll enjoy it.
In my opinion, however, I would forget starting out with making a server and just learn how to use it first. It does make a terrific server platform, but none of it is going to make any sense to you at all if you don't know how to manipulate the OS at all. Learn some of the command line commands, the utilities, the installation, etc. before jumping into a server environment. Redhat/Fedora, SuSe, or Mandrake would be a decent place to start as their installations are fairly straightforward, graphical, detect hardware well, and have user friendly interfaces. There are tons of documentation and support for them too. Once ready for server work, they'll fill in nicely.