There is eating, drinking, dancing and singing with family and close friends. It may be accompanied by the popular "Silvester" custom of Bleigiessen. A small piece of lead will be melted over a flame in an old spoon and dropped into a bowl of cold water. From the shape you can supposedly tell your fortune for the coming year. At midnight, when the old year is almost spent and the new year is about to start, glasses are filled with champagne or wine, and toasts and hugs go with wishing each other a "gutes neues Jahr". Some go out into the streets and listen to the bells ringing throughout the land. Others participate in shooting in the New Year, or put on their private fireworks.
A list of possible lead shapes and their meanings can be found here.
The book has me thinking of making some Apple Strudel for the Holiday. Mmm, been a long time since I've had that.