To answer the question in your subject line; if I assume you wish to transfer your data from your local dev server (VM) to another TurnKey instance somewhere else (e.g. an instance running on Amazon via the TurnKey Hub), then TKLBAM is the easiest way to do that.

If you wish to just collect up your files manually and upload them somewhere else (e.g. shared hosting, etc). Then you will need to manually do that via one of the many possible options. SFTP/SCP is usually how I do it.

To use SSH/SFTP/SCP you will need to know the password of the root user on your server. Unfortunately I can't help you out with that as you would have set it on first boot of your TurnKey VM. If you can't recall what it is, then you'll need to reset it manually. It's a fairly straight forward process, but is a bit of a PITA.

I just did a quick google to see if I could find explicit instructions on how to do that. I found this and although it's for Ubuntu, it should be near enough for TurnKey.

FWIW TurnKey is based on Debian; which Ubuntu is also based on. So if you keep in mind that v14.x = Debian Jessie you should generally be able to find generic Debian info that is relevant to TurnKey via google. Be a little careful following instructions specifically designed for Ubuntu, as even though it's based on Debian as well, it's not binary compatible with Debian (TurnKey is). Many things will work fine (e.g. my link above on resetting the root password). But some others may not go so well. E.g. I would strongly advise against adding Ubuntu PPA repos to a TurnKey (or Debian) server as they can sometimes cause huge issues!

I hope that helps get you going in the right direction.