...is more of a Vaudeville act than a real skill.
How can I learn absolute pitch?
Uh, you can't. Some people(read: professional
musicians, by which I specifically do not mean drummers or the brass) acquire something close to perfect pitch, excellent relative pitch, over time. However, I have yet to meet somebody who recognized notes as quickly or as accurately as a person who was born with perfect pitch.
Or a conductor who did not act like a snotty mass of arrogance and jealousy towards me for being born with perfect pitch. I never said that.
How can my child develop absolute pitch?
Have your child learn to play a string instrument before the age of seven. I learned to read and write music when I was four; I started to play the violin at the age of five. If the theory is true, this helped me to acquire absolute pitch. The violin is more suitable than, say, the guitar because you have to rely nearly completely on your ears to find notes with reasonable intonation. The guitar is better than the piano, because you will tune it yourself.
Is it a useful skill?
As stated above: Nope. Not very.
You could write down every sound you hear, the bus slamming on the brakes, the telephone busy signal, everything - but you rarely need to.
When analyzing harmonics, it can even be distracting; people with perfect pitch always focus on absolute measures and find it hard to think in terms of intervals or chord progression.
Musicians normally learn to identify intervals quickly;
for a long time, I heard, say, a C and an F and then had to fall back on counting to determine it was a fourth. I could tell you every note in a triad, but had to draw the circle of fifths to compute its hamonic functionality. This is the musical equivalent of a NASTY hack.
You die a thousand deaths each time you sing from sheet music in a choir; either you have to transpose to a different key in real time, or you have to watch the choir dropping farther and farther off key every minute - which is like the sound of scratching nails on a blackboard for me.
As you won't always suffer in silence, this also serves to make you the most hated member of the choir / ensemble in a matter of hours.
Doesn't it ever come in handy?
Of course it does - it's talent show material.
And the Dean of our Computer Science faculty, a hobby musician, was impressed because he could not figure out how I do it. He still believes there really is a connection between musical and mathematical talent.
What he might have learned by looking at my test scores:
This is a myth.