Update#2: GvG is now out for the other regions.
Update#1: Shop is now open! Edit: was referring to NA region
However, at this time of writing, the shop is closed and a lot of people were not able to login earlier as reported at Hearthstone subreddit threads. There were similar issues to the Naxxramas launch so it might take a while before you can get your packs. There were quite a few people buying the wrong pack as well so make sure you choose the right one when you get into the shop to make your purchase!
In the meantime, the free arena run (if you saved it) was fine for me and you can also check out the GvG cards in collection crafting mode by searching for 'gvg'.
