The SSID is either broadcast or sheilded, depending on whether the owner wanted to broadcast it or not. Many people often choose to shield the SSID as another layer of security for their WiFi. The SSID is needed to recieve a prompt for security keys, so without the SSID, you're stuck to look for another WiFi signal.
If the WiFi router is accessible to you - that is; you own it - you can access the router's setup page via any computer that is either 1) physically connect via network cable, or 2) connected via WiFi. You will need to point your browser at the router's setup page - often 192.168.0.1 is used. You will be prompted for a username and password. You didn't provide the model number of your router, but according to this Arris Router manual
I found, if it was not changed from the factory default by the user - it will be "admin" and "password" (without the quotes). From here, you would go to the wireless settings to read or change the SSID and security settings.
If the router refuses the admin / password credentials, that means that it has been changed from the factory defaults. It will not be possible to view the router settings, but you can return the router back to the factory settings by locating the reset button on the device itself. With a paper clip or ball point pen, press and hold the reset button for several seconds, then release. This will remove all customizations to the router settings.
Using the manual as a guide, you can edit any of the settings as desired, but you should at least change the login password to something unique and set the WiFi security to WPA with a security key (word) that does not appear in the dictionary. Use WEP security *only* if there is no other type offered, as WEP security can be hack in under a minute or two by computer. As you can see, not broadcasting the SSID provides an additional layer of security. You can broadcast it is you wish.
Finally, record the the IP address, username, password, SSID, security type and key and attach to the underside of the router. Should you forget the info needed to access it in the future, you'll find everything you need on the label.
I hope this helps & good luck!