How to report App Store rule violations?
Apple has implemented many changes in 2017 and 2018 time frame as the size of the store has grown. How you get support depends upon your relationship with Apple.


As a consumer, you would report and ask for support based on purchases you make. As a developer, you have a dedicated channel to report rights violations, fraud, and general concerns.
The App Store is now much better where you can voice critical reviews and get feedback from the developer for all to see. If a major app is doing things that are surprising people, that shows very clearly in the reviews.


But really, unless there's something serious, why wouldn't you just disable notifications for that app, then open a support ticket with the vendor and maybe leave a bad review and delete the app? 

I would expect Apple support to show you how to delete the app and how to disable notifications and then hand you off to the developer if they aren't making you happy.

If you purchased the app recently (which should cover the vast majority of things that are blatantly wrong)


http://reportaproblem.apple.com


Apple's report page directs you to the web page listed for support. Even this page is very carefully shaped to get Apple items like billing and subscriptions handled, but venting / reporting / tattling / complaining about an app isn't something Apple has a web page to receive feedback that's easy to find from the App Store apps or the general support pages.

If you are a developer, sign in and contact support: 


https://developer.apple.com/contact/#!/topic/select




In 2013 - the state of reporting issues was less formalized. The support was more case by case and reviews were one way (Developers couldn't respond to complaints at all, let alone publicly).


You should send a message to the developer (since you are about to poo over their product on the App Store) - give them a chance to make things right since they might have a fix or be able to assist you directly. 
Go into the App Store and rate the app. If you give them one star and a brief review - kill them with kindness: "If only I could ignore the constant upselling of paid upgrades, I might have liked this game"
Look hard at the description in the App Store. If they materially mis-represented the state of the app (say the screenshots are marketing illustrations and not actually screen shots) - report a problem with that purchase from within iTunes. Find that purchase and click the report a problem link. That fires a flag at that item in the store. You won't get a response, but I am confident that in bulk these are reviewed with the most reported problems getting the most scrutiny. That link may pop up a form to add details - if not, it will take you to the website below.
http://www.apple.com/support/itunes/ - Find the section on contacting support and click it.
It takes you to another page - and you will want to submit your detailed feedback to Apple listing the app, the time/date of the violation and the section of the rules you feel are being violated.




At the end of this process, you may also want to take Apple's support survey and ask that they streamline the problem reporting process to make it more clear how / when users should be sending feedback to Apple. You can bet that once enough people start using the tools given and enough complain (politely and with detailed evidence) that it takes too long to report obvious problems with the review tools - it can be fixed.

I do know that if/when your report gets to the desk of a developer support person, they will know how many steps you needed to take to get them the problem report and it's more likely they will dig into it if your complaint has merit.

Most importantly, if you paid money for the app, consider asking for a refund. Detail why the app isn't as described or isn't following the norms you have seen Apple publish and how you feel bad for supporting both Apple and the developer financially when they don't follow the rules set down.

A financial ramification, well reasoned complaints/criticism and using the tools Apple has given for consumers to rate apps together will send a clear signal that the business didn't do a good enough job selling a specific app to you. Once patterns of failures accumulate, they can't go un-noticed.