The answer to your question is not a simple one sentence, or even paragraph answer.

 

Although I have a strong understanding of how an individual transistor works I am having trouble grasping how they work as a circuit. One example is how do they turn DC into AC.

A single transistor is biased so it conducts DC current without a signal. Its output voltage is half the supply voltage so that its output can swing positive and less positive with the signal.
The very old "garbage" circuit was designed for obsolete high impedance headphones so you cannot use it today with modern low impedance headphones.

I am beginning to look at this circuit http://electronics-diy.com/4x4.php Just another simple low current headphone amp.

Its DC current with no signal is low but its AC output current is high enough to drive modern low impedance headphones.

Capacitors are used to remove unwanted frequencies.

No.
There are no unwanted frequencies. We can hear from 20Hz to 20khz and if the amplifier amplifies as high as 100khz then it doesn't matter because music doesn't profduce anything that high.
Nothing in the new circuit removes high frequencies.
C1 is used to block DC from the signal source if it has any DC./ therefore C1 might not be needed.
C2 blocks the DC at the base of the transistor from being drained away by the volume control and also keeps DC out of the volume control would cause crackling noises.

P1 is volume and simply acts as a voltage divider.

Yes.

R1, R2, D1 and D2 are used to supply a bias current so the transistors work at any voltage rather than only activating at above 0.7v, I assume the diodes are in place as a voltage drop but not sure.

The two output transistors operate push-pull. The diodes accurately match the voltage of the base-emitter diodes of the transistors and also change the same with temperature changes. The diodes keep the current from one transistor to the other at a current that is high enough so the transistors do not produce crossover distortion as one transistor turns on and the other transistor turns off. But the current is not too high that would waste battery power and cause the transitors to get hot.

R3 may be another voltage divider.

No.
R3 is in parallel with the headphones so that it charges the output capacitor when the headphones are not plugged in. Then when the headphones are plugged in they do not make a loud POP.
The current of the first transistor is in the speaker since the speaker connects to the positive supply instead of to ground. Then the output capacitor "bootstraps" (look in Google) where the speaker connects to R2 and R3 so that it swings above the supply voltage so that Q2 gets a fairly high swing. The bootstrapping causes a constant AC current in the first transistor which increases its load impedance which increases its closed-loop voltage gain.

As for the placement of Q2 and Q3 I simply cant see the logic in their placement, I cant work out how energy flows through this circuit to give a boosted output.

Almost every audio power amplifier and opamp uses this "complementary emitter-followers" circuit. Q2 pulls up positively and Q3 pulls down less positively.