How can I run multiple unique WordPress sites off of one VPS

Well you have two options, you can either do vhosting and have separate instances for each domain. This would mean the sites would be completely independent from each other. If you’re thinking of selling of a site or moving it to a different vps/server because it’s outgrown the current and deserving of it’s own server. Also some plugins don’t fully support multisites. Drawbacks are this is a high maintance and harder task to do.

Or you can turn your site into a multi site install and then use the Domain Mapping Plugin Pippin has mentioned. This is all round the easier method, you just follow the instructions. And you’re users can use the same account on both sites. Depending on your setup multisites can result in a major pain in the ass. However for most people it’s just fine.