Q:

How do I actually play higher octaves in flute?

Flute newbie here. I'm learning to read notes and play them on the flute (Western concert flute, closed buttons). I find many sources for fingerings of the notes in different octaves. Sometimes they are contradicting and sometimes the fingerings are the same for different octaves. I also know that I can change the octave by changing the air speed. I'm confused about that.
If I see a low C and a high C on the note sheet, how do I actually play them? Do I change the fingering? Or do I change the air speed? 
Some youtube videos show fingerings for higher octaves, and when I try them they sound differently, because I have a different air speed. 
Some other youtube videos mention that the step between C and D is very hard, because you have to move almost all fingers. But that's not true, right? I can also change the air speed and have only a minor change in the fingering?!

A:

In order to answer your questions completely, we must understand a little about how a flute works. Basically (leaving out a few keys for the moment) the modern flute plays the notes in the first octave of its range, from c' (middle C) to c'' (an octave higher), by successively opening fingerholes, effectively shortening the playing length of the tube, and sounding what's called the fundamental tone (also known as the first harmonic).  This is the lowest sound you can get for any given fingering.
Starting with the next tone higher from c'', d'', the sound is produced not by playing the first harmonic, but rather the second, which is twice the frequency of the first, or an octave higher.  That's why you have to move so many fingers going from c'' to d'': you're going from the highest note of the fundamentals, with all fingerholes open, to the lowest of the second harmonics, with almost all fingers down.  Thus, there's no way to get from c'' to d'' with a minor change in fingering- unless you use the trill keys, which are there for exactly that purpose.
You are right about the speed of the air.  The faster and narrower the airstream, the more likely that you will overblow: produce a higher harmonic than the fundamental.  You can do this by simply blowing harder, or by narrowing your lips.
A good way of practicing this is by taking a note somewhere in the middle of the octave- say, G, and playing first a g', then a g'', using only your lips to go up and down the octave.
I hope this helps.

