If you purchase Empires Apart from the Slitherine Store, then you'll want to click a couple of buttons to get your Steam key so that you can download and play the game.
The game can be purchase from the Product Page here:
http://www.slitherine.com/products/product.asp?gid=675
Once you've purchased the game (remembering to use any coupons you may have (like the Slitherine Anniversary vouchers)) then you'll see something like this:
The Download link here, and in your email will point you back to this thread

The next step is to click on the "My Products" link in the header
Which will show you something like this screen.
On Here, click the Get Steam Key on the Empires Apart row. The screen will refresh and your shiny new steam key will be there for you! (It looks like XXXXX-XXXXX-XXXXX)
To add it to Steam, just open it up and select "+ Add A Game..." and then "Activate a Product on Steam...".
Paste your key into the box and Steam will then verify the key and add it to your library for you to download!
Thanks for purchasing the game direct from us, and we hope that you enjoy the game as much as we do
Thanks!