Trying to delete a single SMS text message or iMessage in conversation view in the same way you did with iOS 6? Surprisingly, Apple has changed how text messages can be deleted in the new iOS 7.
First, open your conversation that you wish to delete messages from.
Now, hold down on the message you wish to delete until you receive the more menu.
This will return the familiar radio buttons next to all messages in the the thread. You can select all messages you wish to delete and then click the Trash icon in the lower left hand corner to deleted selected messages. If you wish to delete all messages, click the Delete All text in the top left corner of the screen.
Additionally, you can delete entire threads from all messages view by swiping to the left on the contact name. You will then be prompted with a red Delete confirmation to delete all messages from that contact.