New Year's is called Silvester in Germany. The name comes from Saint Silvester, whom was the Pope of the Catholic Church from 314-335. He is known to have mended leprosy, baptized Constantine the Great, and to have met the recognized members of the family of Jesus.
There will be large fireworks displays throughout Germany, the largest one in Berlin. If you prefer to create your own show, you will be in good company! Many Germans will take the streets and light off their own fireworks, which you can purchase at local groceries and shops starting December 27th.
One of the many Silvester traditions in Germany is Bleigiessen. This is the tradition of foretelling the future of the coming year. This can be really fun for both adults and kids. You will melt a lead form (top hat, clover, horse shoe, etc) on a spoon over a candle and then drop the molten lead into a bowl of cold water. The shape it will form in the water is the basis for the years prediction. If you see a flower it means friendship, a boat means travel, a pineapple is an indicator of a secret love, and a torch means long life. You can purchase the Bleigiessen kits in grocery stores or on amazon. The kits come with the shapes to melt, spoon, and a guide to interpret the shapes.
As for meals, the traditional silvester meal is linensuppe, or lentil soup. Each lentil represents a coin and should bring wealth to you in the new year. Of course, there are always brats, sauerkraut, and sweets to be enjoyed. Carp is also a traditional food and if you carry a scale from the fish with you, it is said to bring good luck.
Check out the British show, "DInner for One". This is the traditional New Year's show and is a 10-minute long comedy sketch. It is always played in Germany on Silvester and is one of the most repeated TV shows in the world because of this. You can watch it here: https://youtu.be/BN9edpdCH7c
Wishing everyone a Happy New Year's, or auf Deutsch, "Guten Rutsch" (good slide)!