Celebrating Noumenia

In his book "Hellenismos Today" Timothy Jay Alexander wrote that the festival "Noumenia" can be celebrated on the first day of a month.
Do you celebrate such a festival? I do not celebrate it at all because I have no idea how to do. On the first day of a month I worship Selene because she is the Goddess of the moon.
How can a Noumenia festival look like?

I myself celebrate the Kalends. 1st of the Roman month.

With appropriate hymns to the Moon, with a special meal, by cleaning up and setting your home in order. In general, setting things up the way you would want them at a beginning, something like a minor New Year's Day.

There is not a specific action that characterizes the day of the New Moon, it is simply the beginning of the next lunar month.

Thank you very much for your quick reply.

The Noumēnia is, besides obviously Selēnē, also sacred to Apollōn Noumēnios, and to the household Gods. A month or two ago I also saw some post on Facebook I think mentioning Artemis Noumēnia. I have found nothing to indicate this is an ancient custom, at least as far as Athenian customs goes. I asked about it in the Hellenic Polytheistic Community on Facebook, and one person replied that it is very well possible, as the Gods presiding over the Noumēnia could apparently vary across the different regions and poleis. Personally I think worshipping Artemis Noumēniē/Noumēnia besides Apollōn Noumēnios could in an case be a useful modern innovation, as these deities are twins who share several epithets. A friend of mine has blogged about this subject, and made an analysis of why she believes it does make sense. You can find her blogpost on the matter here.

If you want to see some ritual outlines for the Noumēnia, here are two examples. The first one is from Hellenion, and can be found here. The second one is by Neokoroi, and is available here.

I don't recall reading of Artemis and the Noumenia or her having an epithet relating to it (whereas Apollon is known as Apollo Noumenios or simply Noumenios). I have seen reference to Hera being associated with the Noumenia (in Rome, Juno was honored during the Kalends).

Does anyone observe the Deipnon and Agathos Daimon as well, or just the Noumenia?

I utilize the Attic calendar for the purposes of calculating certain festival days – but in general use I, and others of my tradition, follow the Orphic astronomical/zodiacal calendar, which is essentially a solar rather than lunar calendar. For me, the Neomenia is the day I clean my home, clean the beeswax and wine spots off of the candlesticks and bomos table, clear out the ashes from the censer, put fresh flowers in the vases, and, most importantly, re-start the recitation cycle of the Hymns, the previous cycle of which I will have finished the previous morning.

In reply to Callisto, yes I observe the Agathos Daimon, but on the day following the Noumenia.

Same here, consecutive nights - the Deipnon then the Noumenia then Agathos Daimon.

I celebrate the Deipnon... it's a good day to clean my altar. I'll light a candle and say a hymn to Hekate. Sometimes I'll scramble an egg up will garlic and leave it at a liminal place for Hekate's supper. On Noumenia I say a hymn to Selene and Hestia.