"Tu" (the Hebrew abbreviation of 15th) in the month of Shvat was set (Hillel's opinion generally overrules Shammai's) as the beginning of the tithable year for tree fruit: Calculating the tithe on fruit starts again for fruit that sets after that date.
The actual Rosh Chodesh celebration is hardly mandated, so there's a lot of room for creativity in designing a ritual celebration. Here are a few ideas for starting your own.
Here is the quintessential Jewish question: How do we emulate God? We are told that we were created by God. We are told that we have a divine spark within us.