Since you're using CentOS 5, the default package manager is yum, not apt-get. To install a program using it, you'd normally use the following command:
$ sudo yum install <packagename>
However, when trying to install git this way, you'll encounter the following error on CentOS 5:
$ sudo yum install git
Setting up Install Process
Parsing package install arguments
No package git available.
Nothing to do
This tells you that the package repositories that yum knows about don't contain the required rpms (RPM Package Manager files) to install git. This is presumably because CentOS 5 is based on RHEL 5, which was released in 2007, before git was considered a mature version control system. To get around this problem, we need to add additional repositories to the list that yum uses (We're going to add the RPMforge repository, as per these instructions).
This assumes you want the x86_64 packages. Test by running uname -i. If you want the i386 packages, replace all occurrences of x86_64 with i386 in the following commands
First, download the rpmforge-release package:
$ wget http://packages.sw.be/rpmforge-release/rpmforge-release-0.5.2-2.el5.rf.x86_64.rpm
Next, verify and install the package:
$ rpm --import http://apt.sw.be/RPM-GPG-KEY.dag.txt
$ rpm -K rpmforge-release-0.5.2-2.el5.rf.x86_64.rpm
$ rpm -i rpmforge-release-0.5.2-2.el5.rf.x86_64.rpm
And now we should be able to install git:
$ sudo yum install git-gui
yum will work out the dependancies, and ask you at relevant points if you want to proceed. Press y for Yes, and n or return for No.