The dark moon is coming up in a few days, and shortly after that we will see the first sliver of the new moon in the sky. I have for a long time made a practice of acknowledging the presence of the new moon in some way, as it marks the beginning of a new cycle of the moon. In folklore it has also long had great significance and I think its important to acknowledge that.
There was a belief that you could tie your luck and wealth to the growing light of the moon by turning any money in your pocket or a ring on your finger when you first saw the new moon and reciting a small chant. This sort of sympathetic magic is simple and easy for anyone to do and represents a common form of folk magic.
Additionally I've found that keeping my eyes out - or rather up - and following the course of the moon throughout the month helps keep my tied to this cycle. The cycle of the moon has always had more power for me than the sun and while I am now shifting into seeing a greater power in the stars the dance of the moon retains its significance as well.
When I see the new moon each month I acknowledge it by kissing my fist in the direction of the crescent and saying something. Sometimes I might say something spontaneous while others I might recite a traditional prayer; there are several prayers to the new moon that we have in Scottish and Irish folklore.
One prayer that I use often which is based on a piece from the Carmina Gadelica is:
"If you have found us well tonight, O Moon
May your light leave us seven times more blessed
O Moon so fair, may it be so as seasons come and seasons go."
Another traditional prayer that I often use, from the same source is this one:
"Glory to you forever
New moon tonight
You are always
The glorious lamp of the poor."
So that's a small sample of my own practices around sighting the new moon. Of course there's a lot more that can be added to this but I think this is a good start for anyone who doesn't do this that might want to consider starting.