A number of people choose to "start" their work with the Moon at the New Moon, for new beginnings and new intentions. This is the way we've chosen to do it on this blog, at least for this year.
Beginning with the energies of the New Moon is a very "western," goal-oriented way to do things. We like beginnings, we like making plans, we like measuring and calibrating and starting over. This cycle begins with the quiet of the dark moon, thinking about what one might want to focus on for the following two weeks until the moon reaches it's peak fullness. Two weeks really isn't a long time to devote to anything; really, it's just enough time to sink your teeth into something, to work with it a little bit, play, and see what comes of it. Once the Full Moon comes, you're supposed to harvest what you've sown, see what worked, and let go what didn't.
It's important to note that that part of the cycle lasts exactly as long as the "work" part. Just like the moon exacts a push and pull on the tides, so can it measure the give and take of our lives. We tend to push, push, push, and not take time to reflect--certainly we don't give it equal measure to our efforts to improve ourselves.
Another way of working with the moon is, in a way, exactly the opposite -- to start with the Full Moon. The Celts marked the beginning of the day at dusk, at the descent into darkness, and similarly, many people find their spirit works best by beginning with the self-reflection and purging rather than the jump into creating something new. After all, isn't the new created from the old, the green shoots of spring rising from the warm decomposition of the previous season?
In this manner, we start by descending into shadow, and seeing what we come up with. What do we NEED to work with? What suggests itself? What do we need to let go in order to make way for something new? Then, in the full shadow of the Full Moon, we can truly begin again, and shake our wet phoenix wings and kick away the ash.
One way isn't any better than the other--it really depends on what you feel most comfortable with. It's probably worth trying both, to see how they feel.