When you view your messages, you should see a small box to the side of each one.
Tick as many of the boxes as you need to, and scroll down. Below the last message to the right you should see a "Mark/Unmark as important", click that and change it to "Delete marked".
From there just click on the box to the right that says "Go". You'll get a message asking to confirm, click yes.
(Or, if you'd like to delete your entire first page of messages, below the "Mark/Unmark as important" box you'll see a "Mark all". Hit that and continue as above.)