Can not send or recieve messages to a person with a non Iphone.

Make sure the contact has a 10 digit phone numnber, not a number without area code.

Can you send a SMS to the phone? Try turning MMS and iMessage off.

Messages won't be received if the other phone does have MMS setup on their cellular service account.

If those ideas don't take care of it, take a look at this Apple doc -> iOS: Troubleshooting Messages

The problem may be on the other end, with the other carrier or phone.

Try changing the 'Start new conversation from' setting to your phone number, in Settings > Messages > Send and Receive.

If that doesn't work, try deleting the conversation in Messages and then creating a new conversation.