The recording below is part of a paid webinar I did recently on integrating a rich Dialogflow chatbot into your website using the v2 API. This particular video provides a high-level overview of how the system works.
The interesting thing about this system is that it can be used with any server side programming language.
PHP based course
If you use PHP for your website, I have created a full course which provides you with all the information you need to add a rich website chatbot to your own website. The course includes code samples, as well as the Dialogflow agent ZIP file so that you can get a basic bot set up and be up and running in a very short time.