Go to your PM page (link under the Welcome message at the top right of any forum page). There's a link labeled "Empty Folder" to the top right of the bar graph that shows you how many messages are in your inbox. Click it.
If you only want to delete a few, click the checkboxes next to the title of the ones you want to delete, select "Delete" from the Selected Messages combo box in the bar at the bottom of the message list, then click the "Go" button.
If you want to delete all but a few, click the checkbox in the red bar above the message list, unclick the checkboxes next to the title of the ones you want to save, select "Delete" from the Selected Messages combo box in the bar at the bottom of the message list, then click the "Go" button.