In a nutshell, retirees and veterans of the military services may join full and part-time installation ceremonial teams (honor Guards) for the purpose of supplementing, not replacing, team members for funerals.
There are two unofficial categories: the veteran joins the team, is suited up in the Class A or Ceremonial uniform and works each day to train and perform. The next category is the veteran service organization (VSO) joins with the installation team at the grave site and while the service members fold and present the flag, the VSO members act as the firing party and possibly color guard.
I had the distinct pleasure of being an AP3 member of the Spangdahlem Air Base Honor Guard from 2009 to 2011. It was a great experience that gave me the opportunity to help the team in many ways.
Ask your local installation ceremonial team or VSO about joining. In the meantime, watch Rendering Honors.