To setup MMS on your Samsung Galaxy S3, please follow the steps below.
- Got to Apps from your home screen
- Tap on Settings
- Tap on More Settings
- Tap on Mobile Networks
- Tap on Access Point Names
- Press on Menu then tap on New APN and type in the APN settings which you can get from your service provider
Make sure that you save the settings before you go back to home scree then try sending MMS from your Samsung Galaxy S III.