Open the Messages app on your iPhone
Tap the conversation you want to manage
To delete a single message: press and hold the message bubble, then tap More… and select the message(s), then tap the trash icon
To delete multiple messages in a conversation: press and hold a message bubble, tap More…, select the message(s), then tap the trash icon
To delete an entire conversation: swipe left on the conversation in the list, then tap Delete
To delete multiple conversations: in the Messages list, tap Edit, select conversations, then tap Delete
To automatically delete messages: go to Settings, tap Messages, then under Message History select Keep Messages and choose a time option
To delete messages by searching: open Messages, use the search bar to find the message or contact, then delete the relevant conversation or message(s) from the results