New Moon and Dark Moon both occur during the same general phase of the moon (The phase opposite of Full), but they represent energies of different qualities. The moon is considered "Dark" during the very last waning days of the moon. The moon becomes "New" at the moment when it passes it's fullest Dark phase (exactly opposite Full illumination) and begins waxing again.
A general rule of thumb when calculating lunar phases is "three days before and three days after". Using this as a rough guideline, the "Dark Moon" would be the three days before, and the "New Moon" would be three days after the actual change of phase.
The Full moon also has waxing and waning aspects. The three days leading up to the full are called waxing Full, and the three days after peak Full are called waning Full.
You can find the actual time of the moon phases in any common almanac, or even on the weather page of your local newspaper. The energies found in the moon phases can be used in many different ways. Some examples:
~Flame RavenHawk