shibby06's answer was about preorders.
For books which have been fully released, it's basically instant: You get access as soon as you complete the purchase, maybe a couple of minutes at most.
It's happened to me more than once that I never received the e-mail, but could still download the book, though.
And the other day (see thread in the Feedback forum), I didn't actually receive digital access to all books. But this was fixed after creating a support ticket.
So basically: If you've completed your order but can't download the book yet, open a support ticket.