The Spanish ñ is pronounced similarly to but not identically with the "ny" sound of "canyon" or the "ni" sound of "onion."
To be more precise, the ñ is pronounced with the tongue more completely against the alveolar ridge (the ridge between the top teeth and the roof of the mouth) than in the English approximation. You might also think of it as pronounced much like the n except by using the middle-front of the tongue rather than the tip. This gives the sound a bit of a nasalized quality. The difference in the sound is very slight although noticeable to careful listeners.
The word and phrase used in the audio lesson on pronouncing the ñ are señora (Mrs.) and hasta mañana (until tomorrow).
The sound of the ñ should not be confused with the sound of the n, which is a separate letter of the Spanish alphabet.