I have a multi site installation and I would like to move an existing site to the multi site installation. I am surprised this isn't in the manual or up on the faq...is this possible? Site is on the same server so I can connect to the database if that helps.

YES this is possible and require manual operation.
The principal consists in installing all the extension required by the website you install as slave site under JMS.
When done, you can create a fresh slave site into JMS without installing it using Joomla installer.
Instead of applying the Joomla installation, you can copy the current "configuration.php" file of your existing website into the deploy directory that you have specified in JMS.
This will re-use your current DB to establish the connection.

If you want, you can also backup / restore your current DB and just change the DB parameters in the configuration.php that you will copy.
Perhaps you will also have to check the tmp and log path present in the configuration.php file.