While I have not had the confidence to use it yet, I currently own a Creality Ender 3 V2 3D printer. This is a pretty basic, low-cost model that is often recommended for beginners and well respected in the creative community. 

It is an open frame unit with the motors moving the print head along the frames, the bed moving forward and backwards as it prints.  The filament hangs above the whole unit, being fed into the print head as it is extruded. In future I may decide to upgrade and purchase an additional, better machine.

A 3D model can be sculpted in a program or simply purchased from a marketplace, at a fairly affordable cost. It can then be altered and sized, then the slicing program will 'slice' the model into layers, which is how the item is printed. It and translates this into coded instructions for the printer, telling the motors how to move the parts. The file can then be put onto an SD card and printed directly from the machine.

When printing, a long plastic filament feeds into the print head, where the metal nozzle heats, melting and extruding the plastic as liquid. The nozzle then moves around the surface, building layer by layer, higher and higher. Each layer cools and hardens as it goes, creating the 3D printed item. The process can be quite a long one, but better and faster machines are available for higher costs.