One of my favourite months for sky gazing is December. Here are some events to note.
Orion is the main constellation one will notice and as I wrote last winter, a reference to Christ's birth, as Orion rising indicates it is winter. Two of the brightest stars in the sky, Betelgeuse and Rigel, are clear in opposite parts of the belt. With the eyes, the multiple stars θ1 and θ2 Orionis, called the Trapezium and the Orion Nebula (M42) can be seen. This constellation helps you find other bright stars, as this diagram from Wiki shows clearly. Orion rises in the east.
The other constellation which is obvious is Cassiopeia. The constellation looks like an upside down "w"in the northeastern sky. The other amazing event involves a meteor shower. The Geminids can be seen on the 13th - 14th of the month. You will have to get up between two and three in the morning to see these. The shower is worth getting up for....wear warm clothes.