It'd be impossible to write a primer about using the internet without explaining what it is. The internet is a vast array of interconnected computer systems, providing an assortment of different services. It's often referred to as the “world wide web” (WWW) or “information super highway” because if you were to draw a diagram of the internet it'd look rather like one of them (interconnections between one thing and another, across and through each other, like a roadmap or a giant spiderweb).
Each thing on the internet has its own unique address, allowing connections to be made specifically to it for some purpose. Connections between yourself and something else go through whatever's between you and them (which is why any confidential information should be encrypted). Whenever you access something on the internet it's a two-way street—you connect to them, make your request, and they send the response back to you. Not only does this mean that you can't really do anything totally anonymously on the internet (their response is sent to you at your address), but most services also log what people do with them (i.e. records are kept).