How can I access Prisoner of Azkaban on Pottermore?

You don't unlock it. It's just like the real thing: you would have to wait just like you wait for the next book or movie.

You can't. It's not out yet :(

U can't unlock it yet... u'll have to wait :)
You can check on the pottermore blog... they update what's happening on pottermore and might have the date of when the 3rd book is coming on pottermore... not sure, but worth a shot ;)