I speak in TCP/IP packets

Your interface with the web starts with a click on the browser; the browser translates this link into an HTTP Request Header, which looks like this:

Get http://neil.verplank.org HTTP/1.0 \n

First, the Domain Name (verplank.org) gets resolved to its IP address (64,81.145.64 in this case). All address on the internet are actually numbers (a lot like a phone system, isn't it?), but someone somewhere invented the DNS (Domain Name Server) addressing system, which allows us to remember the numbers with "helpful" mnemonics like neil.verplank.org.

When you see a message like the following:

Netscape is unable to locate the server: biff.sys.com. The server does not have a DNS entry.

(and how many times have you seen that?) it means that either a) there is no address (number) for "biff.sys.com" or b) at the moment, the internet can't remember where it wrote down the number or possibly c) once again you're connection to the internet dropped when you weren't looking.

Next, the request header gets sent to the server at the IP address, and the server knows, based on the header, what kind of information to retrieve, and how to format its response. It sends said response to the request IP address (your computer) and your internet application (again, be it a browser, fetch, etc.) formats the response accordingly.

All this information transfer happens with packets -- randomly sized chunks of information. Everything going in or coming out of your computer is divided up into these packets, then fired out over the internet. Each packet has a "mailing address" and "return address" (your IP address and the server's IP address) attached, as well as its size, etc.

Actually, fired would be a nisnomer. If you're using a 56K modem, you're sending and receiving information at 56,600 bits per second, or 7.2K per second (optimally). Compare that to your had drive, which is moving informational back and forth to your computer at as much as 10MB/second, or about one thousand five hundred times as fast.

The internet moves those packets along whatever path it sees fit. Each computer along the way looks for the shortest/least busy path towards the end computer, and sends the packet along, after some chit-chat and maybe a cup of coffee, of course. The internet is nothing if not polite. The sender, which is both you and all the other computers along the way (hops in the route), keeps track of which packets it's sent that have been received. Anyone in the chain will resend packets a certain number of times until complete failure results, and your browser gives you an error message about TCP/IP or broken pipes.