In the Messages app?
There is no easy way to delete/clear all the messages at once.
You can delete entire conversations at once. In landscape view, tap the Edit button at the top left, tap to select each conversation, then tap the Delete button at the bottom of the conversation list.
If you have a recent version of iOS you can go to Settings > Messages and change the Keep Messages to 30 days or a Year. This should immediately notify you that older messages will be deleted, and then do it automatically from then on.