The problem you've got is that there's no skill that exists for Alexa to allow it to connect to Ring.
In addition, even services like IFTTT that support both devices only allow you to use them as an input to the system.
So you could do something that works when you say something to Alexa, like turn on your lights. Or you could turn on your lights when someone rings the bell.
But you can't get Alexa to "say something" if ANYTHING happens (let alone if the doorbell rings) just like you can't control Ring to do anything if you turned on a smart light.
Both devices (currently) appear to only work as inputs, neither have any outputs or controllable actions.
Saying that, that's all I can see from googling. Once you plug these things in sometimes auto discovery gives you extra options that are so user friendly no one documents it.
However, if you can't get it to work then there's every possibility there's nothing to get working.