Installing the FreePBX application
FreePBX is a program that works together with Asterisk and a number of other programs to make it easy to set-up and configure a VOIP PBX. By itself, FreePBX won't do anything. You also need to install Linux, Asterisk, Dahdi, Postfix/Sendmail, TFTP, and a host of other programs.
If you are not an expert with Linux and its dependent components, you'll want to choose and install a Distro. If you are an expert, you can simply install FreePBX on top of an existing Linux/Asterisk installation.
The Easy Way (use a Distro)
There are a number of distributions ("Distros") available that will automatically install include FreePBX, Linux, and all the other components you need. When you use a distribution, you avoid having to learn how to install, compile, and configure each of these required components. A good distribution comes with everything you need to get started.
There are several distributions available, including the FreePBX Distro, PBX In A Flash, AsteriskNOW and Elastix. The easiest way to install FreePBX is to download the FreePBX Distro from the download page. For step by step instructions to install the FreePBX distro, click on this link: Installing the FreePBX Distro
If you have a stock Centos 6.3 or 6.4 system you can convert the machine to the Official FreePBX Distro by following these steps.
For information on the release versions and how to upgrade the FreePBX Distro read Upgrading the FreePBX Distro.
Be sure not to confuse "FreePBX" (which is a program) with the FreePBX Distro (which is a distribution that includes FreePBX and all the other stuff you need).
The Hard Way
The hard way to install FreePBX is to set-up a machine running Centos, Asterisk, and all other required applications, and then install FreePBX manually.
First Steps After Installation
For some suggestions on what to do after you finish the installation read about the First Steps After Installation.