The Noumenia is celebrated in the night the moon first becomes visible after a dark moon, which is this Thursday. I celebrate the Noumenia in the context of the Neokoroi ritual (visit at http://www.neokoroi.org) which means I have a small ritual in which I have a libation to, among other Gods, Apollon Noumenios. The other libations are to Hestia, Selene, Agathos Daimon and all the Immortal Ones.
Besides the libation and standard ritual, I also use this day to deeply clean the room where I keep my altar (which will vary depending on whether I am in Lisbon or Castelo Branco) and clean the altar and images of the Gods.
In the context of Apollon cult, Apollon Noumenios is celebrated as a God of purification and renewal, whom purifies so we can star anew and kills all unnecessary. Another aspect of Him I find present in Noumenios is light bringer: the moon will again reflect the sun and cast light upon the night, and as the new month starts we ask Apollon to guide us with His light.
This is essentially a day when we renew our vows towards the Gods and honor them all with offerings, hymns and libations. It is primarily a family / private ritual, but because our community is so small it can easily be adapted to a community festival.