It is indeed possible for one not born with absolute pitch to acquire it through extensive ear training and practice. I do not know all of the pitches, but I can use deduction to figure out the rest*.
The same goes with chords.
So, how does one acquire absolute pitch?
- Get a keyboard or instrument that is not easily detuned nor out of tune (a detuned instrument tends to completely destroy one's ear training).
- Begin by playing the note that is most important for your core instrument. For example, guitarists should pick E because E is an important note on the guitar. Pianists should pick either A or C. People who play instruments in concert pitch should choose Bb. And so on and so forth.
- Begin by playing that note. Over and over. Sit there for at least fifteen minutes playing the note in whole note intervals (of rhythm) until the pitch is indelibly burned into your memory.
- Play the major chord on that note. Languish in the texture. Feel the emotion. Play it until you know it cold.
- Play a note dissonant to the first. Play it mostly, but alternate to the first or the previous notes you have been trying to memorize every once in a while. Playing a dissonant note from the current one you are trying to learn helps one notice the difference between the two. Notice the imaginary pulsing beat between the two in your mind (imagine playing the two notes at the same time).
- Do the same thing with chords.
- After you have done about three notes/chords, stop and try imagining them in your mind. If you can without any problem, start on other chords (minor, diminished, augmented, sevenths, ninths, etc.) or notes.
- Always be sure to imagine them in your mind. This is key. Always do this. Do some interval training as well.
- Do the previous for at least half an hour a often (it isn't important to do it each day; just like lifting weights, it is good to do it a few times a week). In a month's time one should be relatively familiar with each note. In about three month's time, one should have absolute pitch.
Of course, there are multiple methods to ear training. This is the way I used, and it seems to work pretty well. Over a much longer period, however, musicians tend to get more accustomed to pitch naturally, and long-time musicians often have absolute pitch (sometimes acquired).
The pitches I have trouble with I can figure out by taking C (my core note) and matching it up to the note I am figuring out. By imagining both in my mind, I can "see" the dissonance and discover the interval. By adding the interval to the core note, I get the note I am trying to discover. (this only takes a few seconds and becomes better with time, especially with a sound ::cough, cough:: music theory understanding)
Also, be sure to play musical "mind games" with yourself every once in a while. Try to imagine what two chords layered on top of each other would sound like. Try to imagine what C half-sharp (half-sharps do indeed exist) would sound like. And so on and so forth.
* Apparently, that means I have some combination of relative pitch and absolute pitch...