how does the coffee shop guy (the WIFI host) see what i'm doing on my computer?

When you request a web page, the HTTP (Hyper Tex Transfer Protocol) request are sent to the web server hosting the web page.

This request passes off a firewall installed on coffee shop.

The guy just see log filtered by the firewall and he knows what you are doing.

You can use proxies some how to protect your privacy.

Good luck my friend.......

Well it's probably un-encrypted wi-fi, so anyone with the right gear can see what it transmitting to and from your computer. Also, there would be logs on the router of what was accessed.

You are using his router. He can install some software to log down all in and out traffic through his router, except you buy some WiFi protection like
http://articles.winferno.com/windows-security/wifi-protection/
http://usatoday.jiwire.com/top-wireless-tips-wifi-security.htm

Yeah, if he wants to, I guess. He could always use custom firmware on his router to log all HTTP traffic, for example.

Or, if there's no encryption, he could intercept your HTTP packets and get all your passwords.

I doubt he's doing that, but you never know.