The New Moon or Dark Moon is the end and the beginning of the lunar cycle.
Rituals about forgiveness are performed during the New Moon. It is also a good time for scrying, especially if you are looking for long held secrets or you need new information about something in order to move forward in your life.
New Moon water to be used later for banishing spells can be made now. Put water into a glass jar, add a piece of black onyx, put the cap on and put the water outside during the New Moon. This is actually best done for three days, starting two days before the New Moon, so I'm afraid that I did not give you any advance notice about that one. Try it next month.
But here is a tip on time. Prosperity spells are best started the day after the New Moon. If you need to do one of these, plan for it today and do it tomorrow.
I don't have any special rituals that I perform during the New Moon, but since I was a small child I liked to go outside on a clear night and watch for the hazy glow around the edge of the Dark Moon. It is quite lovely.