sudo mv /filename /etc/init.d/
sudo chmod +x /etc/init.d/filename
sudo update-rc.d filename defaults
Script should now start on boot. Note that this method also works with both hard links and symbolic links (ln).
At this point in the boot process PATH isn't set yet, so it is critical that absolute paths are used throughout. BUT, as pointed out in the comments by Steve HHH, explicitly declaring the full file path (/etc/init.d/filename) for the update-rc.d command is not valid in most versions of Linux. Per the manpage for update-rc.d, the second parameter is a script located in /etc/init.d/*. Updated above code to reflect this.
Also as pointed out in the comments (by Charles Brandt), /filename must be an init style script. A good template was also provided - https://github.com/fhd/init-script-template.
Another link to another article just to avoid possible link rot (although it would be saddening if GitHub died) - http://www.linux.com/learn/tutorials/442412-managing-linux-daemons-with-init-scripts
As pointed out in the comments (by Russell Yan), This works only on default mode of update-rc.d.
According to manual of update-rc.d, it can run on two modes, "the machines using the legacy mode will have a file /etc/init.d/.legacy-bootordering", in which case you have to pass sequence and runlevel configuration through command line arguments.
The equivalent argument set for the above example is
sudo update-rc.d filename start 20 2 3 4 5 . stop 20 0 1 6 .