How should a GFCI be installed according to the NEC?
The NEC isn't the right place to look for this stuff
The reason you couldn't find anything that answered this question in the NEC is stated right up front in NEC 90.1(A) (quoting from the 2014 edition, italics mine, italicized text new in 2014):

90.1 Purpose.
(A) Practical Safeguarding. The purpose of this Code is
the practical safeguarding of persons and property from
hazards arising from the use of electricity. This Code is not
intended as a design specification or an instruction manual
for untrained persons.

Instead, you want to look at the installation instructions that the manufacturer provides for a given GFCI device.  This is enshrined in NEC 110.3(B):

(B) Installation and Use. Listed or labeled equipment
shall be installed and used in accordance with any instructions included in the listing or labeling.

However, I'm not sure if that's a sufficient answer for your quiz.  If it's not, most receptacle and deadfront devices do install similarly -- your input conductors terminate on to the LINE-side screws (black/brass is hot and silver is neutral, as usual), while loads downstream of the box can either be fed from the LOAD terminals if they need protection or from pigtails off the LINE terminals if they don't.  Grounding and pigtailing is the same as a standard receptacle otherwise.  Breaker-type GFCIs install like a breaker, but have a pigtail or clip that attaches to the neutral bar, and then an extra lug for the load neutral to land on (if you try to wire the load neutral to the neutral bar, the GFCI won't ever reset as it won't be able to &quot;see&quot; the current returning back from the load).
As to testing? There's one correct answer, and that's to use the TEST button on the device.  This creates a path from load-hot to line-neutral (or vice versa) through a current-limiting resistor that is a &quot;controlled leak&quot; for the GFCI to sense and trip on.