Although the graph of a parametrized surface can be viewed and manipulated on the computer screen as a surface in 3D, it is not quite suitable for printing on a 3D printer since such a surface has zero thickness, and thus it does not correspond to physical object.
To produce a 3D printout of a surface, it needs to be endowed with some "thickness". To do that, we move every point from the surface in the direction of that point's nomral vector by the amount ±T/2, where T is the desired thickness. The locus of the points thus obtained forms a thin shell of thickness T around the original surface, thus making it into a proper solid. The result then may be saved into a file in the STL format and be sent to a 3D printner for reproduction.
The worksheet attached to this post provides a facility for translating a parametrized surface into an STL file. It also provides a command for viewing the thickened object on the screen. The details are documented within that worksheet.
Here are a few samples. Each sample is shown twice—one as it appears within Maple, and another as viewed by loading the STL file into MeshLab which is a free mesh viewing/manipulation software.
Here is the worksheet that produced these: thicken.mw