Subscribers won't receive activation keys, but instead user name and password! Only offline sales, Bitcoin sales, and promotional subscriptions include activation keys, which have to be entered manually.
The activation of regular subscriptions instead happen automatically after purchasing on exactly the account used during the purchase. If the client does not reflect the activation, you are most probably not logged in with the account originally used when purchasing the subscription you want to use now. To start using the Premium service, all you need to do is to log in with this account. For that open the side menu and click on 'Use different account'.
IMPORTANT: To use a subscription always login with the credentials of the account, you originally have used while purchasing. If it was a newly created account, you should have the user name and password in your email (in case you did not save them).
If you lost or wish to recover your account, you can always use the Oops, I forgot my password URL from the account login page.