Robby is correct that the communication happens in packets, but not really detailed.
The Internet network works much like a road network and is navigated in the same way. Except, on the Internet, the crossroad decides which way you should take.
If the computer you are talking to is very close to you, the data just travel to the ISP, then directly to its destination.
If the computer you are talking to is in a different city but still belongs to the same ISP, the data go to the ISP server local to the source computer, then travels across the ISP's network to the ISP server local to the destination, then directly to the destination.
The ISP' network can have various topologies, but it is built to handle the data transport requests efficiently. Wiring all pairs of customer hubs is not efficient. Connecting all hubs to a single server might be efficient, but it quickly overloads the central server as the ISP grows bigger. Often, the ISP's network is a tree (much like the road network in a small village) if the ISP is small enough.
The ISP is connected to other ISPs near it. If the computer you are talking to is a few countries away, the data has multiple paths to take, and picks the fastest one, with regard to contention.
For example, if Poles are watching their own citizen getting nominated a pope (which happens in Italy), the data might travel from the TV camera in Vatican to an italian TV broadcasting company as a video signal, then converted to bytes, sent to the company's ISP, then within that ISP's network to a austrian-italian boundary, then to a czech-austrian, then to a server owned by a czech ISP and located somewhere in southern Bohemia, then to Prague (where the ISP's headquaters are), then finally towards Poland where a polish ISP handles the data and sends it to everyone's homes.
But, if Czechs are watching their own guy singing or swimming or getting killed, the czech server tells the italian server, "Hey, I'm overloaded. send the the thing elswhere", and the austrian server sends the thing elswhere (say, Slovakia or Germany).
If newyorker watches the pole poped, the options are few but very thick.
Say you wanted to get from Vatican to New York by car, and there was a tunnel from Glasgow (Great Britain) to Halifax (Canada). You'd have to get to the Channel Tunnel in france, ride it to the Great Britain, take the highway to Glasgow where you enter our hypothetical tunnel, then from Halifax to New York along the shore (stopping in Boston).
It turns out there is an internet cable from Europe to America. More exactly, there are several of them ( http://www.cablemap.info/ ), and more are getting laid. So, our data packet travels across Italy to France, across France to Plerin, France where it gets converted to light (if the french ISP uses metallic cables) and beamed to Northport. One more hop to a New York's local ISP, then to the client. If the cable gets broken or congested, the data routed through UK and then some other cable.
The cable Plerin-Northport is a real fiber-optic cable, named FLAG Atlantic (FA-1).
Most often the Transmission Control Protocol (TCP) is used. for every data packet that gets sent through the network, a smaller one travels back to acknowledge its arrival. If an acknowledge is not received by the sender in time, the sender sends a new packet with the same data.