If you've been allocated Artillery it is supposed to be available after 2 minutes.
Usually it seems to take a lot longer than that, but maybe that's just frustration. When it does become available you will receive verbal confirmation and the 'Artillery' icon at the bottom left of the screen will become coloured.
When you decide to use the Artillery just click on the icon and left click on the target area.
**** WARNING **** You only get one strike during each engagement AND they are not really accurate so keep you own troops away from the targeted area.