How to create live user chat for website?

I have my website already but I would like users to be able to chat to other users like with Facebook chat i.e. when a user gets a message, a small chat box pops up at the bottom of the page which can then be closed when the user is finished with it. 

I have never used c# on a webpage before so I am unsure how to complete such a task. I have looked at some existing methods such as SignalR but I was wondering if the user has to run this from the c# application which would then open the webpage? I do not want the user to have to run the application, I would just like them to be able to log into the website and start using it. 

What methods should I be using and what steps should I take to get this done?

Thanks,