The alpha testing will come when they’re ready to release it. In the meantime, you can pass the time by playing the pre-alpha version which has been out for 20 years. 
If you have the original game and haven’t yet bound your codes to your Blizzard account, you can do so by going to your Blizzard account overview and entering the game keys from the box into the “Redeem a code” field.
If you don’t have the original game and want to play NOW!!11, you can pick up the game+LoD expansion for $20.
Under “Classic Games”.
If you do decide to play the original game, I highly recommend using Sven’s Glide Wrapper. I’ve posted a setup guide to aid in getting it working.
Also if you do play the original game, if you use a VPN service, be sure to turn it OFF when playing on Battle.net! Also public/business connections are not allowed. (Either will cause a two-week restriction from Battle.net access in Diablo 2)