It works quite a lot like using a hot glue gun. The nozzle goes back and forth on the X and Z axis, while the tray moves up and down on the Y axis. It just lays down very thin layers of the materials in the 3D shape required. It's a very interesting process, most civilian models these days are limited to using ABS plastic, which isn't the best material in the world, but there's also the possibility of using advanced polymers or even liquid metal. It's generally a very efficient process, slow but there is very little waste. You can do things with additive construction that you cannot do with subtractive construction, stuff like print a wheel with ball bearings inside it, or a solid hollow cube.
The technology has so much potential, not quite a Star Trek replicator, but it could conceivably get to the point where if you want a chair you load the program and set it to print before you go to bed, and when you wake up it's done including screws and other fasteners and you just need to assemble it. Want a fork, you can print a new one, need a straw so you print one of those too, along with a plate and a cup. Have an idea for something, model it out and print it. No more looking around for something that might not be manufactured anymore, break an old picture frame and print a new one rather than spending your life searching garage sales and flea markets. If something breaks you could print a replacement. With the right materials there are very few things that could not conceivably be printed, but right now a lot of the more advanced stuff is still in the prototype phase or very expensive.
Entry level printers roughly cost a bit over $500. The RepRap project is working on designing a printer that can print other printers to make them self replicating. I think they said they were at over 50% self replicating capacity as of last year.
Sci-fi has been on to the idea for decades, it could conceivably get to the point where you could start with a printer the size of a suitcase and a truck load of spools of wire, or containers of powder, or liquid, or whatever medium your material comes in, and eventually print yourself an entire house. All you'd need is the printer and the raw materials. Print some 2x4s, print some nails, print a hammer, print some insulation, print some plastic moisture barriers, print some exterior sheeting.
Sure people will look at some cheap novelty printed in ABS plastic and say it sucks and it'll never be the equal of traditional machining, but people were saying the same thing about every new technology for as long as there have been people. You can be damn sure that when NC machining first came around people were saying it was a gimmick and it'll never equal a manual machinist, and now it's taken over the market. Look at how the government barely recognizes email as a valid form of communication, and it's been around for decades now.
