From the inbox view, long-press one message and you'll see the Trash Can icon. Tap this icon to delete the message.
You can also set Delete as a swipe option (Settings > Swipe Options), then use your finger to swipe on the mail you would like to delete.
To delete a message from an open email view, tap the Trash Can icon at the top of your screen.
Deleted messages will be moved to your Trash folder.