To archive a message, simply right-click a message and choose ‘Archive’ as shown below.
Alternatively you can use the 'Swipe to Archive’ gesture. To do this, put your cursor over the message and swipe two fingers from the left to the right of your trackpad. You should see a grey area appear on the left side of the message, keep swiping your fingers until the grey turns light blue as shown below.
You can use the "Actions" to configure the swipe actions for Airmail.