|How can I be sure he isn't able to see what I am doing on my computer?|
that depends on your friends computer sophistication and how the hookup to the modem is made. Odds are you have nothing to worrry about.
Networking is pretty easy once you understand the physical connections and why. MS has included a networking wizard, which with the help of a usb stick, will get you and your parents pc up and talking in no time.
Google is your friend. Lots of online how to's including screen shots.