How could one celebrate Rosh Chodesh at home and are there any customs like on Shabat (candles, bread, kiddush) or festivals (blowing shofar)?
You should have a bigger, nicer meal. (Shulchan Aruch Orach Chaim 419)
Add hallel in davening and ya'aleh v'yavoh in Shmoneh Esrei and bentching. (SA OC 422 and 424)
Some women have the custom of not doing melacha. (SA OC 417)
Other than that, not really.