Start with google - there are loads and loads of examples of chat room software out there. Pick one you like, and use it. After that, all you have to do is ensure that the conversation is stored somewhere while it is going on - Cookies, Session or Database depending on how permanent a record you want - and then generate an email at the end and send it.
The only specific bit I can give you is the email - which is a simple method:
Sending an Email in C# with or without attachments: generic routine.[
^]
The rest of your question is too vague and open to be answered specifically.
Submit an article or tip