The message "connected, no internet" usually indicates a captive portal. In short that means you are connected to the router, but without your first "identifying" to it it won't "let you out" but rather "holds you captive".
In modern Android versions (Android 6 and up at least), Android detects this situation by itself (hence the message) and offers you to "identify" to the portal (it shows you a notification to tap on):
"No Internet" / Captive Portal (source: Wikimedia, click to enlarge)
If that does not happen, simply open your web browser and try to open a page, e.g.
www.google.com. Your browser then should automatically take you to the login-page of the portal first.