3d prints work off of 3d models.
There are a few techniques to do this. One like above uses layers of melted plastic, like normal printing but with an added demention.
The second way is to use a special resin liquid and high intensity, focused UV light to harden the resin within itself.
The first way is by far the most popular and yields the highest resolution. There is an entire community based around 3d printing and a moment for open source hardware(like coat hangers, parts, cases, cups, dishes, etc.).
It isn't too hard to make a 3d printer either. RepRap and a few other DIY printers along with blue prints and schematics are available. Go to hackaday.com and search 3d printers. There are hundreds, that won't cost an arm and a leg to make or buy. People also offer print jobs, send them your 3d models and they'll mail you the print.
I am very envoys though that you have access to production grade printers though.