In short, on a Unix-based system, you can download the Git source code from the Git Download Page, and then run something along the lines of :
$ make prefix=/usr all ;# as yourself
$ make prefix=/usr install ;# as root
You will need the expat, curl, zlib, and openssl libraries installed - though with the possible exception of expat, these will normally already be there.
If you are running Linux, you can likely install Git easily via your native package management system:
$ yum install git-core
$ apt-get install git-core
If that doesn't work, you can download the .deb or .rpm packages from here:
If you prefer to install from source on a Linux system, this article may be helpful:
Article: Installing Git on Ubuntu
In both Mac 10.4 and 10.5, you can install Git via MacPorts, if you have that installed. If not, you can install it from here.
Once MacPorts is installed, all you should have to do is:
$ sudo port install git-core
If you prefer to install from source, these articles may be helpful:
Article: Installing Git on Tiger
Article: Installing Git and git-svn on Tiger from source
With Leopard, you can also install via MacPorts, but here you have the additional option of using a nice installer, which you can download from here: Git OSX Installer
If you prefer to install it from source, these guides may be particularly helpful to you :
Article: Installing Git on OSX Leopard
Article: Installing Git on OS 10.5
On Windows, installing Git is pretty easy. Simply download and install the msysGit package.
See the Git on Windows chapter for a screencast demonstrating installing and using Git on Windows.