How can I add control points to the default 16 control points of a NURBS surface?
"Extrude Curve and Move" or "Subdivide"
You can add control points to a NURB surface object by running the command Extrude that you can find in the modeling section of the Tool bar in the Tool shelf and then move le vertex away with grab. Or you can do all at once with the operator of the title (shortcut E).
The operation is very similar to the one you can perform with meshes, but this is for surfaces only (UV coordinates only).
If you want to increase the resolution while keeping a similar shape of the grid, you can use the Subdivide operator (you can find it in the Toolshelf too). Subdivision cannot break the NURBS's laws, so you should select a whole U (or V, or both) stripe to make it work.
Remember that NURBS modeling tools in Blender are not currently (2.76) as advanced as the Mesh counterparts, so some functionalities you expect may be missing.