Open the Settings app
Tap Messages
Tap Blocked Contacts
Tap Add New
Select the contact to block
To block a specific number from a text thread: open the Messages conversation
Tap the contact name or number at the top
Tap Info (i)
Tap Block this Caller
Tap Block Contact to confirm
To block an unknown number: open the Messages conversation
Tap the number at the top (or the contact name)
Tap Info (i)
Tap Block this Caller
Tap Block Contact to confirm
To manage blocked numbers via the phone app: open Settings
Tap Phone
Tap Blocked Contacts
Tap Add New
Select the contact or number to block