If we are running a server that is not attached to the domain, how would I go about adding a domain user to a local group on that server?
You don't. There has to be a trust between the computer and the domain (aka joining the computer to the domain) to be able to authenticate domain users locally.
Now for something practical:
You have two options 1) create a local user with the same username and password as the domain user, and add that local user to the local group. 2) Join the machine to the domain.