December
This is the month in which the classic constellations of the Winter are rising, most notably, Orion. This is a real favourite because of its abundance of very bright stars. Take the opportunity to reacquaint yourself with M42, the Orion Nebula.  Taurus will be even higher in the sky now and it is worthwhile seeking out the Crab Nebula, M1. This is the remains of a supernova explosion (see Aries , Spring 1997), at the centre of which is the first pulsar to be seen in visible light (at least as far as I am aware, it was the first). Unfortunately, this is beyond the reach of amateurs. The bright star Capella is now very noticeable, together with the rest of the constellation Auriga. Capella has long been known as a spectroscopic binary star but in 1998, a team from Cambridge used state of the art technology to see its companion using the technique of interferometry. Within the boundaries of Auriga lie the star clusters M36, M37 and M38. These are well worth seeking out though they can be awkward in instruments of less than 50mm aperture. M36 is the smallest, with around 60 stars of mags. 8 - 13.
Mars is now setting early whilst Jupiter and Saturn are clearly visible in the south before midnight. If the computer program I have is accurate, the Moon should pass close to Jupiter on the 17^th and Saturn on the 19^th. Venus is visible in the morning sky, unmistakably bright.
The Geminid meteor shower is usually good and peaks around the 13^th. Its normal limits are 7^th  - 16^th Dec.
January
Facing southwards, the most prominent constellation is Orion. It is easily recognisable because of the 3 distinctive bright stars which for the asterism of Orion's belt. Orion is also easy to spot because it is the only one in the northern hemisphere to contain two first magnitude stars. Top left is Betelgeuse, a red giant star whilst bottom right is Rigel, which is much whiter in colour. Remember to look for

The southern view , mid-January (map produced using Skymap Pro5).

M42, the Orion Nebula, which is the birthplace of new stars. With a moderate sized telescope, look for the trapezium within this nebula. Down and to the left of Orion lies the unmistakable Sirius - the dog star. This is reasonably close to us, a mere 26 LY away. It has a white dwarf companion, the Pup, which is hard to spot owing to the glare of Sirius. Sirius is the brightest star we see, apart from the Sun. Since it is always rather low in our skies, the thickness of atmosphere through which the light must travel, causes Sirius to twinkle violently on most nights, changing colour rapidly. North east of Orion lies Gemini, with the two bright stars of Castor and Pollux, the twins of mythology.  Search out M35, an open star cluster at the feet of the Twins. The end of the month will be good for deep sky observing since the moon will not interfere.
On the planet front, Jupiter and Saturn are still visible throughout the evening and are moving progressively west, setting earlier and earlier. The are found below the constellation of Andromeda. Venus should still be  visible (to early risers) in the morning sky.
February
The arrival of February sees the constellation of Cancer high in the sky. This gives an excellent opportunity to observe Praesepe, the Beehive cluster, object no. 44 in Messier's catalogue of fuzzy things in the sky! From a dark site it is visible to the naked eye. It is also known as the manger (from which the asses - g and d Cancri feed). Galileo observed this with his telescope and counted 36 stars in the cluster. Using 10 X 50 binoculars, around 75 are visible. It was well known in ancient times and was used as a means of weather forecasting:
A murky manger with both stars [g and d] shining unaltered is a sign of rain - Aratus.
A further object, M67, is visible as a nebulous spot in binoculars. It is an open star cluster and a red and orange star can be resolved using a small telescope. Between Cancer and Orion lies Canis Minor, the lesser dog. Its main feature is Procyon, the 8th brightest star in the sky. This, like Sirius, is a difficult double, it has a magnitude 9.5 companion. It took the 36" Lick telescope to see this in 1896. Also becoming visible this month is Leo, on of the classic spring constellations. Insomniacs could spend some time observing the large number of deep sky objects associated with this constellation in the clear winter sky.
During February, Venus will be lost to our sight and Jupiter and Saturn will be setting before midnight.