Open the Messages app
Find the conversation containing the text message
Swipe left on the conversation and tap Delete
Open the conversation if you want to delete a single message
Press and hold the message
Tap More
Select the message or messages you want to erase
Tap the trash icon
Tap Delete Message
To delete multiple conversations, tap Edit in the Messages list
Tap Select Messages
Choose the conversations you want to remove
Tap Delete
Confirm the deletion if prompted
To erase all messages from a conversation, open it, tap the contact name or number at the top, then tap Info if shown
Scroll to the message history options if available
Delete the conversation to remove all messages in it
To automatically remove old messages, go to Settings
Tap Apps or scroll to Messages
Tap Messages
Tap Keep Messages
Choose 30 Days or 1 Year