3D printing involves taking designs from your mind and putting them into the computer via CAD. Then you create instructions so a robot can produce that design from undifferentiated material. Ideally, you start on paper with concepts and dimensions. Then, you use your favorite CAD program to draw your design in 3D with accurate dimensions. Any CAD will do, but solid modeling programs work best. Once your design is ready for the first prototype, you output a Standard Tessellation Language (STL) file that describes the relative shape of your design. That STL file is opened in the 3D printer's control software where you can make decisions about its construction like quality, density, and material. The control software outputs a set of instructions, a.k.a. GCODE, that is loaded into the machine to start the print. After some startup checks, the 3D printer will produce your design on its own. The machines lays down material one layer at a time, incrementing the height of your object layer by layer to produce the full size model. Once the print is done, there is some post processing required to make your model finished and accurate.
In the image above you can see the process of taking Jefferson's new logo with gradient and making a 3D printed model. In the top left corner, the CAD file is shown with a slight curve designed in to mimic the logo's gradient. In the bottom right is a screenshot of the 3D printing software Cura showing the toolpaths the 3D printer will use to make the model. Finally in the bottom left, you can see the completed 3D print.