How does individual computers and server computers interact on the internet?

Imagine this.

----------------
| | I want... ---------------
| | <------------------------- | |
| | | |
|Web Server| | |
| | Here is... ---------------
| | -------------------------->
| | --------
| | Your Computer
----------------


Say you type in google.com.
Your browser sends out a message going from server to server, looking for that address (the "I want...").
When it reaches google.com, the server sends back the correct page to your computer (the "Here is...").

It's more complicated, but this is the basic idea.