Start with the OSI model and approach it like your would eat an elephant; layer by layer.
First bit of homework; tell us how many layers there are and what each does.
Of course there's the whole "OSI model or TCP/IP (aka Internet) model?" debate to be had.
For the OP, the following is a really, really basic overview, omitting/simplifying loads and being closer to the TCP/IP model than the OSI model:
If one thinks about a connection from a home PC to a website (I'm going to ignore wireless here), first you have the connection from the computer to the router. This will be in this example by a network cable.
Down that cable are a stream of bits of data with error correction to guarantee that what leaves the computer arrives at the router intact. This is the physical layer, it says nothing about where the request is going, what sort of request it is etc. It's just concerned with getting from one point to the next, the data to the router. There is another physical layer connection from the router to the exchange down the phone line, and so on.
Encapsulated into that you have something that says where the request is going, by providing an IP address (or other identifying mechanism), followed by the request itself. This means the router can decide if the request is to another device on the local network, or needs to go to the WAN (the Internet), and then send it down the appropriate route (hence, "router"). This is the network or internet layer.
Then one needs some way of determining that this information arrives in order if it needs to, and establish a means to request bits that are missing and so on, and generally enable the two sites to exchange data in a meaningful way. This is the transport layer. Common transport layer protocols are TCP and UDP.
Then there's the actual data that the two computers want to exchange. This is the application layer. Examples include HTTP (the mechanism by which web pages are requested and delivered), SMTP (the mechanism by which email is sent and received into mailboxes) and IMAP and POP3 (mechanisms by which email that has been delivered is retrieved from mailboxes where it is stored).
From your question, it sounds like you are interested in the network layer (in the OSI model possibly the data link layer as well, since routers and switches can also operate at that layer).
I am not a networks person, I'm a programmer, so my terminology is probably all over the place. Someone who actually works in this field will be able to explain it better.
