From a Home screen, navigate: Apps icon > Messages. If Messages is unavailable, tap the Dropdown menu (located in the upper-left) then select Alphabetical. If still unavailable, refer to Manage App Icons.
From the Inbox, tap the Menu icon (located in the upper-right).
Tap Delete threads.
Select the message(s) to delete. Selected when an X is present. To select all messages, navigate: Menu icon > Select all.