Need assistance with patching standalone system (newbie)

Hello,
I am completely new to the world Linux and if it wasn't hard enough, my first real interaction with this OS is a standalone system that has no internet access but needs to be patch on a regular basis to meet government requirements. I am currently running Red Hat Linux Server Enterprise 6.6. I am certain that it is 64bit as well. I have browsed the patch/errata database, but I do not have the faintest clue or idea which patches I need to install. I have tried to install one, but it fails stating that I need dependencies. I was wondering if anyone can provide instructions on how to install patches. I am only focused on security patches because they are the most relevant. For example, RHSA-2015:1623, I would like to patch my system with this patch, however under the x86_64, I have no idea with rpm package I would install on my system. I also read that I need to make sure that all previously errata are installed as well. Can anyone please help?