*Be careful there is no "undo" button and deleted messages are not recoverable.
To delete an individual message: open the conversation thread, scroll to the message you wish to delete and long click on the text. A menu will appear above the message and you can choose Delete.
To delete an entire conversation thread: open the Inbox, scroll to the thread you wish to delete but do not click the thread. Instead, swipe your finger from right to left on the thread you wish to delete. This will open a menu and you can select the red Delete button.
To delete multiple conversation threads: Tap any icon to select messages (a), Begin selecting messages and tap "Delete" (b)