C# Sockets for Game

So I am trying to figure out how to send information(like player coordinates, health, etc) from one client to another (peer to peer or server/client; doesn't matter). What is the methodology to do so?

What I mean is: I can code a console based P2P chat program. That is a no-brainer. However, I want to make a graphical program (using windows forms/XNA) and want to be able to move a character around the screen. How would I take care of making the connection? Meaning: the users will have to type in the desired IP address somehow. Would I use a separate Console? Would I use IO? If so, how would I do all of this?

I am very new to sockets and such and have NO idea as to a good way to create a connection and manage a connection for a program that isn't in console.

EDIT:

I don't want it to appear as though I don't know a thing about C# or programming in general. I am extremely compitent with C# and have been using XNA to learn how to manipulate graphics on a screen. After messing with some socket/type things using console I wanted to integrate a very simple communication between clients into a very simple XNA game project (like seeing other clients move a character around a screen [or only one other client if using a simple P2P])