How to Ask Someone to be "Friends" over the Internet

I teach people how to feel comfortable greeting each other. But how do you greet and introduce each other over the Internet? I am on all the social media and find it stressful to respond to someone that emails with a standard request to be a friend or be "linked-in", without providing any information of who they are or how we are connected. I also don’t know the polite way to respond when I have no memory of ever having met them. I want to be kind, and I know as a professional speaker, an audience member is sure I will remember them. I therefore feel rude not linking or "Friending," but if they don't say they were in my audience, I don't know.
So here are my questions for today.
First question: What is the proper etiquette of requesting to "friend" or link?
Second Question: How can you politely ask, “Who are you? and “How do I know you?”