The New Moon is very prosperous, healthy and lucky time. It is custom to go outdoors to "greet" the New Moon, to go watch it. You can ask the New Moon for health and wealth for example in the following way:
In your left hand, have salt or bread. In your right hand, have coins or a copper object. Chant:
    Terve, terve, uusi kuu Sinä täydeksi, minä terveeksi Vanha kuu sairaaksi Uusi kuu terveeksi Uusi kuu, terve kuu Vanha kuu, sairas kuu Uusi kuu, onnikuu Rahakuu, rauhakuu Tällä kuulla tavaraa Sä uusi kuu nyt anna Suolaa, leipää pivossa Ja kuparirahaa tiuhuaan Anna sä uusi kuuni | Hail, hail, new moon May you be full, may I be healthy May the old moon be sick May the new moon be healthy New moon, healthy moon Old moon, sick moon New moon, luck moon Money moon, peace moon On this moon, items Give to me, new moon Salt and bread in my palm And copper money so frequently Give to me, my new moon |
And this is just one example, probably the most common chant is just uusi kuu sairaaks, minä terveeks ("may the new moon be sick and I be healthy") or something equally short. But I wanted to include the much nicer words here! :) I probably should also mention that the greeting terve (translated as "hail" here) literally also means healthy (which is also the origin of the English word "hail").