With Amazon, if you buy either the standard or the collector's edition, you will be emailed your beta key within five business days of your purchase. The offer will be extended to all existing preorders and will expire Sept. 17. It's only valid on products shipped and sold by Amazon.com.
GameStop offers a very similar promotion, but if you buy the game in-store, your beta key will be printed straight onto your store receipt when you place your preorder. If you buy online from GameStop.com, the code will be emailed to you within two business days of your purchase. Just like Amazon, this offer is valid for either the standard or the collector's edition.
Unfortunately, at the time of writing, it doesn't look like Amazon has rolled out this offer to stores in the EU, and GameStop U.K. doesn't even seem to have Mists in stock. If we hear word that this changes, we will of course let you know!
[Thanks for the tip, Kamaron!]