When you pronounce /n/ as in sin, kin the tip of your tongue is at the t-point of your palate above the teeth.
When you pronounce /ng/ as in sing or king your mouth is opened wide, your tongue is not raised , your throat is wide open as in a long /a:/
and when pronouncing /n/ or /ng/ some of the airstream passes through the nasal cavity.
Wikipedia has an article about Velar Nasal, but I find it totally confusing. In any case you can pronounce the sound /ng/ alone and hold it
in the same way as you can hold the pronunciation of a long /a:/ . When you pronounce /a:/ your throat is wide open and the airstream passes
without any hindrance.
When you pronounce /ng/ you have a narrow passage in your throat, but I can't describe how it is done. I hoped to find something
useful about the articulation of /ng/ on the Internet, but I did not find anything useful.
Edit: Here's another video about /ng/. Perhaps it helps. For me this demonstration is didactically helpless. She talks a lot, but you see nothing.
But as it seems, the back of the tongue seems to form a narrow passage in the throat. http://m.youtube.com/watch?v=qhTSVdjVf14
Edit 2: Now I have found a diagram of the tongue position.The tongur is draw babck a little to form the narrow passage in the back of the mouth