As wingrider suggested, I would first check to make sure your cellular data is turned on:
Settings - Cellular - Cellular Data - On
And also make sure your MMS messaging is enabled:
Settings - Messages - MMS Messaging - On
If both of them are on but it's still not working, reset your network settings:
Settings - General - Reset - Reset Network Settings(it won't delete your information, you might have to enter your wi-fi password again after the reset)
Dmitriy