How can I install git on RHEL 6?

It's a problem with your YUM repo for the actual distribution... It doesn't appear as though you have a "base" repository, based on your yum repolist command output. I suppose you could just download it as well...

[root@Kitteh ~]# yum repolist
Loaded plugins: fastestmirror, security
Loading mirror speeds from cached hostfile
 * base: xt.lol.net
 * epel: mirror.cogentco.com
 * extras: xt.lol.net
 * update: xt.lol.net
repo id                             repo name                                                                 status
base                                CentOS-6 - Base                                                           6346
epel                                Extra Packages for Enterprise Linux 6 - x86_64                            7858
extras                              CentOS-6 - Extras                                                            4
rpmforge                            Red Hat Enterprise 6 - RPMforge.net - dag                                 4445
update                              CentOS-6 - Updates                                                         665

...and proof that GIT is part of the base repository...

[root@Kitteh ~]# yum info git
Loaded plugins: fastestmirror, security
Loading mirror speeds from cached hostfile
 * base: xt.lol.net
 * epel: mirror.cogentco.com
 * extras: xt.lol.net
 * update: xt.lol.net
Installed Packages
Name        : git
Arch        : x86_64
Version     : 1.7.1
Release     : 2.el6_0.1
Size        : 15 M
Repo        : installed
From repo   : anaconda-CentOS-201112091719.x86_64
Summary     : Fast Version Control System
URL         : http://git-scm.com/
License     : GPLv2
Description : Git is a fast, scalable, distributed revision control system with an
            : unusually rich command set that provides both high-level operations
            : and full access to internals.
            : 
            : The git rpm installs the core tools with minimal dependencies.  To
            : install all git packages, including tools for integrating with other
            : SCMs, install the git-all meta-package.