Q. How do computers send data through the Internet?
A. Computers send information through the Internet by dividing the data to send into small chunks ("packets") and transmitting them to the other device. All this happens without your doing anything - the web browser, e-mail program, etc. all take care of these low level details.
When your computer wants to send to another computer, it creates the packet, then places the other computer's address in the destination address of the packet, places its own address in the source address of the packet, and then sends the packet off, either directly to the destination computer, or to a nearby router that takes responsibility for routing the packet.
There's an analogy with the post office here. Packets are like envelopes, with destination addresses and return addresses. Routers are like post offices: they check the destination address and have the responsibility for delivering the packet to the final destination computer or to another router that's closer to the destination.