*picture shamelessly stolen from everythingicafe
So, this is probably going to be a split between talking a little bit about Open Source Media Center and actually installing BitTorrent sync. The first gen Apple TV is actually a miniature computer running a modified version of OS X 10.4 Tiger. It has an Intel Pentium M Processor and an Nvidia GPU, making it easy to hack (Much unlike the Third Generation Apple TV). It is not terribly powerful, especially when compared to devices like the Raspberry Pi, but it served its time. I'm basically using an old one for a mobile media device for our trailer, so we can watch Movies and TV Shows without an internet connection, and without the need of importing it into iTunes or paying for a Plex Subscription for local syncing.
The Apple TV running OSMC is a 32 bit device, meaning you must download the 32-bit version from the Sync Website. The 64-bit version will not work!
You can copy & paste or type the following lines into your terminal, this should download and prepare btsync.
tar -xzf BitTorrent-Sync_i386.tar.gz
mv btsync /usr/bin/
chmod +x /etc/rc.local
Now, BitTorrent Sync listens on the loopback device by default, so you specifically have to add the argument "--webui.listen 0.0.0.0:8888". To start it on boot, we will have to modify /etc/rc.local to start btsync on boot.
sudo nano /etc/rc.local
Add the following line above where it says 'exit 0'
/usr/bin/btsync --webui.listen 0.0.0.0:8888
After that, press Control-O to save, and Control-X to close the nano window. Reboot the machine either through the interface or by typing 'sudo reboot', and the client will start on the next boot.
Grab the IP Address, and in a web browser navigate to [OSMC IP ADDRESS]:8888/gui/, and you'll be prompted with a setup screen. Fill out the forms, and I would recommend you to set the default directory to /opt/btsync/. You will have to manually change the folders in OSMC, but you shouldn't have any weird file-permission errors.
After setting up your hostname, username, and password, you can add the Apple TV as a Read-Only (Or Read-Write) folder in Sync, and transfer TV Shows, Movies, and Music over automatically! If you have any problems with these instructions, feel free to email me!