Instantiate a git repo:

$ mkdir alice

$ cd !$

$ git init

Add a remote:

$ git remote add origin URI_OF_REMOTE

Change a remote:

$ git remote set-url origin NEW_URI

A remote can be a server, it can be a local directory, an NFS share, pretty much whatever you want.

It is a Git convention that the primary remote is called origin. You don't have to call it that, but it's pretty common.