Please look at first two comments to the question. The comment by InsertCleverUserName suggests what you could do, but by comment should explain to you why you should not look for the "manual" teaching you how to do something which is described by your own requirements. And, more generally, it is very impractical to look for manuals in some application field. Instead, you should look for manuals in general programming and some specific fields of programming. In all cases, it should not be about chats. This approach could be way more productive, because your bigger goal is hardly making one specific chat (again, what you want is not a "chat"), but learn how to develop software and complete software projects.
So, in your case, assuming you know general programming and .NET well, further reading may include:
http://www.asp.net/get-started[
^],
http://www.asp.net/mvc[
^],
http://www.asp.net/web-pages[
^],
http://www.asp.net/entity-framework[
^],
http://www.asp.net/identity[
^],
http://www.asp.net/signalr[
^],
http://www.asp.net/signalr/overview/signalr-20/getting-started-with-signalr-20/introduction-to-signalr[
^].
As to SignalR, you need to start with understanding of its value as a
push technology. Please see:
http://en.wikipedia.org/wiki/Push_technology[
^],
http://en.wikipedia.org/wiki/Pull_technology[
^].
This CodeProject article can be very useful:
Asp.Net SignalR Chat Room[
^].
—SA