Regarding the capacitor, Ignacio beat me to it. shakefist
You'll see capacitive coupling all over the place in circuits like these.
As far as what you feed in, actual amplification will depend on the resistor values. The specs say -.3 to vdd (your source voltage) + .3V, so provided your VDD is >= 3 volts, you should be able to amplify to that level.
update
You can simply leave the V01 disconnected. The speaker wire connected to pin 5 in that schematic would be connected to ground instead.
That said, the configuration shown in the schematic is said to have a gain of $$2(\frac{R_i}{R_f})$$ This is because the outputs are 180 degrees out of phase with eachother, so that even though both amplifiers being unity gain (when Ri = Rf), it winds up doubling the input.
If you don't use pin 5(V01), you'll need to adjust your gain. The new formula would be $$\frac{R_i}{R_f}$$
That said, if you haven't already ordered a different chip, I think the LM4880 is more in line with what you want, it's mentioned in the automatic switching circuit in the datasheet, and it's a single output headphone amplifier.
Although it is desirable to bias electrolytic capacitors with a DC voltage they will work without problem with zero bias. The aluminum oxide layer that acts as the dielectric is created during manufacture and is fairly robust and long lasting.
They will even survive a short amount of low level reverse bias although it is not recommended.
Electrolytic capacitors can blow up if reverse voltage is applied or excessive bias in the correct polarity but in general that will only happen if there is enough current to cause significant power dissipation such that the device heats up significantly.
Best Answer
As long as the DC level is positive, the AC amplitude of the audio signal is of no consequence because it is a "coupling" capacitor, in the sense that the RC time constant is much higher than the highest 1/f of the audio signal (excluding dc of course), so the capacitor never gets "charged up" to the audio ac signal voltage (only to its dc value). Instead, the voltage across its terminals remains approximately constant. In other words, the capacitor rides with the input, and if the RC constant was not high enough, audio would be distorted. For example, you could have 1V of dc offset and 10V of ac amplitude. If RC is high enough, the voltage accross the capacitor will ALWAYS be very near 1V,NOT 11V to -9V as the comment to the first answer seemed to imply. Hope this helps.