To buy the premium subscription, navigate to your in-app profile. You will see the "Subscribe" button in there. Press it.
In this window, press the "Try for free" button to activate your trial subscription that will change to the paid one automatically after the end of the trial.
Premium subscription will be automatically activated after the trial period and will be updated every month. You will get the information about your subscription at your e-mail that is linked to Apple ID.
Beware that you are not able to make a refund for subscription, you already paid for. You can read more about it here.