Yes, Apple notifies the user about the upcoming renewal. According to the Apple developer page that talks about subscriptions:
Auto-renewable subscriptions give users access to content or services from within your app on an ongoing basis. At the end of each subscription duration, the subscription will automatically renew until a user chooses to cancel it
In your app you can also point the user to the Apple page that points to the subscription management part in iTunes. This way the user can check on the status of all their subscriptions.
While this isn't an extremely complicated process to understand, I wouldn't call it simple. I've had to go thru several tutorials before I was able to understand it better. Apple has a bunch of info on their Developer site, too.
Updated based on comments: That page links to several other developer pages. Those pages indicate that Apple will try to auto-renew the subscription at the renewal date and will not prompt the user for additional input unless there's a problem (source):
The renewal process begins with a “preflight” check, starting ten days before the expiration date. During those ten days, the App Store checks for any issues that might delay or prevent the subscription from being automatically renewed—for example, if the customer no longer has an active payment method, if the product’s price increased since the user bought the subscription, or if the product is no longer available. The App Store notifies users of any issue so that they can resolve it before the subscription needs to renew, ensuring their subscription isn’t interrupted.
During the 24-hour period before the subscription expires, the App Store starts trying to automatically renew it. The App Store makes several attempts to automatically renew the subscription over a period of time but eventually stops if there are too many failed attempts.
The user can also disable automatic renewal and intentionally let the subscription expire, then renew it at a later date, creating a longer lapse in the subscription. Make sure your app’s subscription logic can handle lapses of various durations correctly.
My reading of that info indicates that the app will automatically renew without user intervention if they have not turned off the automatic renewal feature.