Constructive interference:

Above is an example of Constructive interference of a wave, it is tough to see but right at the beginning the wave is much larger and this is where the two waves came together to make a big one, they combined. You can see it goes back down and seems to “split” into two waves, they are actually just continuing onward.

Destructive interference

Above is an example of Destructive interference of a wave.  It is hard to see but midway through the video the spring is completely flat and then moves again. Two people pushed the spring in opposite directions with the same force making the spring flat when the two waves created, met.

Standing waves

Above is an example of a standing wave. A standing wave is where the waves that hit each other are the same in amplitude and their wavelength and what is observed looks almost like it is stuck in place and there are points that never move, the ones closest to the middle.

How do noise cancelling headphones use wave interference to eliminate unwanted sound?

They have microphones that detect the frequency of noise outside the ear-cup and create very similar sound waves and this cancels out the outside sound. This is called Destructive Interference.