I'm not actually a huge fan of running things like ffmpeg on servers without good reason, but the popularity of extensions such as hwdMediaShare means that sometimes you have to install it.
Normally, it'd be a simple yum install ffmpeg but as it's not really server software it's not in the default repositories, this documentation explains the steps needed to install (without compiling from source). It's CentOS 5 specific, but should actually apply to 6 as well so long as you add the 5 specific repos.
First we need to add a couple of repositories
nano /etc/yum.repos.d/dag.repo [dag]
name=DAG RPM Repository
Next we grab the RPM
rpm -Uhv http://apt.sw.be/redhat/el5/en/x86_64/rpmforge/RPMS//rpmforge-release-0.3.6-1.el5.rf.x86_64.rpm
For some, running yum install ffmpeg ffmpeg-devel will now be successful, for others there'll be a dependancy issue with libedit. If you fall into the latter group, try the following steps
#Add the EPEL Repo
rpm -Uvh http://dl.fedoraproject.org/pub/epel/6/x86_64/epel-release-6-8.noarch.rpm
yum install libedit ffmpeg ffmpeg-devel
That should be job done. Of course, if you are wanting to run HwdMediaShare you'll probably also want to run
yum install mencoder