Updated below with official Blue Post from Blizzard
This evening Blizzard confirmed that public access to the Warlords of Draenor Alpha Test had begun, with invites going out to a limited number of press and World of Warcraft subscribers/account holders. The number of invites given out this far appears to be limited and concentrated to North America, but some EU account holders are known to have received invites.
The best way to check your status is to either boot up the Blizzard Launcher desktop application or checking your Battle.net account through the web portal, where you'll also be able to opt-in to testing if you hadn't already. Some e-mails have gone out but not to all active Alpha accounts. Note that there are currently no 'Alpha Keys' being distributed, accounts are being flagged for access directly.
At present testing is limited to the Frostfire Ridge zone and only the Horde faction content. No doubt additional content will be unlocked over the next few months, but the pre-release process will certainly be a marathon rather than a sprint. The test is currently not under NDA, so streaming and uploading video content to Youtube etc. is pretty much assured.
Be aware that over the next few weeks the number of scam/phishing emails advertising a position on the Alpha test will increase by orders of magnitude, so be ever vigilant and don't click the links!
Update:
Warlords of Draenor alpha invites have gone out to a small number of individuals for our first phase of external testing, historically dubbed “Friends & Family” for its limited scope of availability to Blizzard employees’ friends and family, as well as some streamers, press outlets, and fansites. Alpha testers are free to share screenshots and videos, stream content, publicly discuss their experiences in the alpha, and offer their feedback in the Alpha Feedback forum.
This initial wave is extremely limited, and we’ll be sending additional invites as testing progresses. In the meantime, we recommend visiting your favorite fansites for information and updates, Twitch to watch streams, and the front page here at WorldofWarcraft.com for continuing content updates. You can also check out the full alpha patch notes right here!
Please be aware that no keys are available for the Warlords of Draenor alpha, so be on guard for potential scams using invites as a lure. You can always check to see if you’ve been invited by logging into your Battle.net account at http://www.battle.net and viewing your available game licenses. You’ll never need to click on a link in an email to redeem a testing invite for Warlords of Draenor. Visit our security site for information on how to identify and avoid scams intended to steal your account information.
If you’re interested in participating in future testing phases, you can opt in here to World of Warcraft and other Blizzard game-testing opportunities. Additional invite opportunities will be announced as they become available, and we recommend checking back regularly for updates.
This initial wave is extremely limited, and we’ll be sending additional invites as testing progresses. In the meantime, we recommend visiting your favorite fansites for information and updates, Twitch to watch streams, and the front page here at WorldofWarcraft.com for continuing content updates. You can also check out the full alpha patch notes right here!
Please be aware that no keys are available for the Warlords of Draenor alpha, so be on guard for potential scams using invites as a lure. You can always check to see if you’ve been invited by logging into your Battle.net account at http://www.battle.net and viewing your available game licenses. You’ll never need to click on a link in an email to redeem a testing invite for Warlords of Draenor. Visit our security site for information on how to identify and avoid scams intended to steal your account information.
If you’re interested in participating in future testing phases, you can opt in here to World of Warcraft and other Blizzard game-testing opportunities. Additional invite opportunities will be announced as they become available, and we recommend checking back regularly for updates.
So essentially this phase appears to be baldly represented as a Press Alpha not covered by NDA. That's a major departure from Blizzard's past treatment of WoW expansion testing phases, and mirrors updated policy from Heroes of the Storm. Exposure is also important due to another major MMO release this week and announcements at E3.
Source: Battle.net Official Forums
