This can be as complex as you want to make it or fairly straight forward. There are a couple ways to go about it. We've had a lot of our clients in Columbus, OH and Dublin, OH start asking us about ChatBots so we decided to do a quick intro here.
Fully Custom ChatBot
1) You can code and tie together all the free third party services and build a bot that way integrated into Facebook. It would take a bit of effort to go this path. The long and the short of it is there are 3 different pieces that need built, the bot itself usually using googles AI free service, server code to understand what to do w/ the conversation, and then the integration into Facebook. I'm really watering that down, but the short answer is , if this needs done quick, probably not the best route. If you were building an actual bot for a business that services customers, this is ultimately the right solution.
Quick and Easy ChatBot Implementation
2) There are a few services out there that package up everything into one service, one that stands out is https://chatfuel.com/ it will do everything for you just by giving the Facebook account permissions to it. They give you tools to build out the AI part of it and give it general keywords to look for and how it should appropriately respond and it handles the natural language processing. There is a fee with this, I believe its around $30 / month.
Hopefully that gives you a quick idea of complexity and a quick way of implementing a ChatBot into your website.