One way is to go to OpenELEC settings and do enable auto update.
IDK if you looked at wiki, but the first method for manual update is very simple and easy. Download openelec 6.0 and place the tar file in the update folder, reboot and at it will automatically update to the file you placed in update folder. To access openelec on you chromebox type: \\192.168.1.1 and replace the IP with your chromebox ip.
The update function in openelec won't update you from 5.0 to 6.
So you will have to use the manual update option. Easiest and quickest way is copy the tar file you downloaded onto a USB stick. Plug that into the chrome box and use the file manager to transfer the file to the update folder under root in the file manager. Reboot you box and it will update and erase the file on its own.