After a lot of searching and asking here, I managed to get it working:
Before doing the following, make sure that you aren't using
unison-gtk (the Unison GUI) as well. I've had a situation in which
unison-gtk conflicted. Remove
sudo apt-get remove unison-gtk, and disable Unison's old config files by renaming the containing folder:
mv .unison .unison.old
When you've done that, it's time to move on.
First I ran the script as a superuser. I did that because Unison needs to be run once when you create a new script, to make some logging files. The Upstart-scripts are probably run as root, so it's best to do that too when you run the script for the first time:
unison -perms 0 -batch "/home/MyName/Syncfolder" "/mnt/Data/Syncfolder" >> /var/log/unison.log
Then, I ran:
sudo gedit /etc/init/unison.conf. I pasted the following, and saved the file:
description "My File Sync"
author "My Name"
start on runlevel 
echo "Starts syncscript"
echo "Ends syncscript"
exec unison -perms 0 -batch "/home/MyName/Syncfolder" "/mnt/Data/Syncfolder" >> /var/log/unison.log
Restart and you're done.