GIT is a distributed version control system. You can find more informations about it on http://git-scm.com/. There are tutorials, downloads etc…
Using it is very easy if you understand how GIT actually work and the concept of distributed version control systems. To do that it is very good to spend one hour to watch Tech Talk: Linus Torvalds on git video in which creator talks about it.
It is very important to fully understand how git works and how to use it.
You cannot use GIT like CVS or SVN, and better do not use IDE plugins (like egit or jgit for eclipse). If you do, there is a big chance that you will get rid of GIT too soon, thinking that this SCM is shit. And the fact is that you just misused it.
As for free git servers I know that there are several. I am using google code for my all projects (works with hg too).
I have created page with most useful GIT commands here. I will most probably extend the list of commands since I am still new git user, and I am learning.