So a friend set my computer up, he happens to run networks and has a private one of his own.
Will he be able to see my computer and what i'm doing?
The easiest way for your "friend" to do that would be to install a program on your computer that he would be able to connect to. Likely also he'd have to configure your router, assuming you are using some form of broadband, to allow the incoming connection to your machine.
However, with the way most networks are set up today, a person can't just "see" what you are doing without some cooperation with your router and computer.
It's possible for someone to create a program that does things like record what keystrokes you are typing and send them without your knowledge, and other nasty things. If your router has "remote management" enabled, he might be able to log in to that via the Web and look at your router's logs and things like that. There's worse things as well.
The moral of the story is that you shouldn't have someone you don't trust doing work on your computer.
If you are really paranoid I recommend you read the manual to your router, learn some basics on configuring it, reset it, and reconfigure it yourself. The router is the gateway from the outside Internet into any computer within your home network and if you reset and reconfigure it yourself, you'll know the main path into your home network is set up by someone you trust, i.e. yourself.