How do I enable SMS messaging on my iPhone?

If you are having trouble with sending/receiving SMS, then contact your carrier. That is a service your carrier offers. You can choose to fallback to SMS when an iMessage does not go through, but the SMS messaging is still done by your carrier. There is not a setting on your phone to enable/disable SMS messaging, but there is an option to enable/disable MMS messaging, which is just an SMS message that includes pictures or videos.

The setting to fallback to SMS when using iMessage is only for sending a message, it has no effect on receiving a SMS message. Is your trouble with sending or receiving?

Go to settings>messages then turn on send as SMS.