Within a few years, 3D printers will be nearly as common as paper printers. So we'd best learn a bit about them. A 3D printer, as the name implies, prints in three dimensions. If you remember the old "dot matrix" printers, or have looked inside an inkjet printer while it's working, you'll have seen a physical print head moves back and forth as the paper moves up. That is 2D printing: back and forth, and, up and down, are the two dimentions. Now imagine the paper flattened out, and the print head moving back and forth as well as left and right - this is how old style mechanical pen plotters moved in 2D. Now imagine the print head can move up and down as well as front to back and left to right, and you've got 3D. Change the ink to molten plastic and you've got an idea how most consumer 3D printers work. More expensive commercial units can print with molten metal.
The idea is not new; it's been around for several decades. The main credited inventors are Hideo Kodama of Nagoya (Japan) Municipal Industrial Research Institute and Chuck Hull of 3D Systems Corporation (USA). Hull's contribution is the design of the STL (STereoLithography) file format that is widely used today. The first widely-known do-it-yourself printers are from the RepRap project (started in 2005). RepRap intends to provide self-replicating printers, i.e., those that can print all their own parts. Since some of the parts need to be metal rather than plastic (for accuracy and for strenght), we're not there yet. As of 2015, some projects based on RepRap have reached about 75% of the self-replicating goal.
Just as you have to format a document before printing it in 2D, you have to design or model your object before you can 3D-print it. Or, as you can photocopy an existing document, you can 3d-scan an object, clean up the file, and print from that. There are dozens of software tools, both free and open source, that can be used for these operations. There are also sites such as thingiverse.com (funded by MakerBot Industries, one of the original makers of 3D printers), where you can download models of "things" to print, share new designs, modify existing ones, and so on, all for free.
The RepRap projectis still going strong and, for those who want to build a printer completely from parts, is probably still the best bet. There are also numerous commercial printers, many of them based on the RepRap software (and sometimes even the hardware). MakerBot and Ultimate are examples here. These are usually available fully-assembled, ready-to-print; some are also available in kit form. One interesting variation is Freaks3D from ElecFreaks, a design firm in China. Available assembled or in kit form, the Freaks3d is portable, so you can more easily take it to schools, to trade shows, or to your friends' house. This is the printer that your obedient servant started with. You can read more about 3D printing at Wikipedia. A news site with lots of coverage is Notey.com
3D Printer Manufacturers
Several e-tailers sell 3D printers, including http://www.robotshop.com/en/3d-printers.html
Numerous companies supply the "ink", known as "filament" because it comes in long thin shape, usually 1.75 mm in diameter. The two most common types are PLA (poly lactic acid, biodegradable) and ABS (harder plastic, longer lasting, higher melting point). Be sure you get a type that your printer can use! No point trying to keep a list of filament suppliers up to date; just do a web search on Google, or Amazon, or even Kijiji Classifieds, for, e.g., "abs filament [name of country]" or "pla filament [name of country]" as a appropriate. Note: Quality is far more important than price, so check the reviews!
There is a ton of information online, some free and some not:
3D Printers, like any tool, can be used for good or bad. Hammers can drive nails but also break bones. Cell phones can help you stay in touch, but can also be used by kidnappers, drug cartels, and others for nefarious purpose. Guns can kill and guns can defend against killers. 3D printers can repair things, or make things to help you break things. Such is the nature of the human psyche.
And so it is possible to 3D-print a small gun like a handgun or an AR-15 rifle, using ABS plastic, but the gun can only be fired a few times before it breaks. In the U.S.A. and possibly other jurisdictions it is apparently legal for a person to manufacture their own gun in this way. There is at least one company making a 3D milling machine that lets you make the part of the gun that really has to be metal; you can find them on the internet.