To change the SSID and/or the wireless password on the ZyXEL VMG1312 you will need to access the router interface through a web browser. To do this make sure you're on a device that is connected to the router, open a web browser, and then type the IP address of the router (192.168.1.1 by default) into the address bar then press enter. You will then be asked to log into the router.
By default the username is admin and the password is 1234, but the password should have been changed during the setup of the router.
Once logged into the router hover over the "Network Setting" option on the bottom menu and the select the "Wireless" option from the popup menu.
Once in the wireless section of the router you will see "Wireless Network Name (SSID)" below the heading "Wireless Network Settings". Change the value in this box to change the SSID. Here you can also choose whether to broadcast the SSID or not, set the maximum number of devices allowed to connect wirelessly, and the maximum download/upload bandwidth allowed for wireless traffic.
At the bottom of the page there is also the "Security Level" section. Changing the security level will change the wireless security mode (none/WEP/WPA2), it is advisable that you leave it on "More Secure" if all of your wireless devices support WPA2.
To change the wireless password un-tick the "Generate password automatically" box and then enter the password you want into the "Password" box. You can tick the "password unmask" box if you wish the characters to be visible.
Once you've made the changes you wish to make scroll down to the bottom and click "Apply".