A few hints even before you step outside: wrap up warm, and allow time for your eyes to adjust to the dark. Lots of loose layers of clothing trap heat close to the body; gloves and a hat are also essential. And you need at least 20 minutes for the pupils of your eyes to open fully so that you are properly dark-adapted.
Even with the unaided eye there is a lot to see at the moment. You can start by using the prominent figure of Orion the hunter - centre-stage in the south - to lead the way to less obvious constellations. Extend the line of his "belt" upwards, and you hit the V-shaped Hyades star cluster. This is the "head" of Taurus the bull, distinguished by the bright red star Aldebaran - the bull's baleful "eye". Two enormous horns protrude from the bull's head. If you extend the line of the belt downwards, you reach the constellation of Canis Major, the great dog - and Sirius, the brightest star in the sky. From these latitudes it is always low in the sky, and we see it through many layers of our shifting atmosphere. Like hundreds of moving prisms, the restless air cells constantly bend and focus the light of Sirius, making it flash all the colours of the rainbow.
If Christmas delivered a small telescope or binoculars to your door, the winter sky can be even more of a treat. Go back to Orion's belt again and look below at his "sword". You will immediately notice that one of the stars there is fuzzy. In fact, it isn't a star at all - it is the Orion Nebula, a glowing cloud of gas that is part of a huge star factory. It has already given birth to a clutch of baby stars which make it glow like the gas in a neon tube.
Humble binoculars, having a wider field of view than a telescope, are great for sweeping the winter skies. You will pick out countless groups and clusters of stars, strewn and scattered across every inch - especially towards the band of the Milky Way. But the sky-sight for binoculars has to be the Pleiades, just above the head of Taurus. Tennyson described the "seven sisters" as looking like "fireflies tangled in a silver braid", and through binoculars the compact star cluster - comprising more than 300 stars - is a gem to behold.
You can use binoculars or a telescope on the next celestial sight - the furthest object you can see with the unaided eye from the British Isles. The Andromeda galaxy is an independent city of stars like our own Milky Way - but is more than 2 million light years away. Look between the square of Pegasus and the W-shape of Cassiopeia to find the misty oval, bigger in extent than the full moon. A telescope or binoculars will show a brighter concentration of stars towards its centre, but only the biggest telescopes in the world can reveal individual stars - and then only the brightest of the 400,000 million that make up the galaxy.
From the most distant object visible to the unaided eye, we finally go to the closest - the Moon. Only 385,000km away, our nearest neighbour in space is sensational when viewed through binoculars or a telescope. But do not be misled into looking when the Moon is close to full early in the month. That is when sunlight falls almost flat on the Moon's disc and there are no shadows to pick out the relief. Towards the end of January, when the Moon is between a crescent phase and first quarter, the light falls sideways on, creating a dramatic landscape of stark light and shade. Binoculars will show countless craters and the vast, lava-filled plains that make up the face of the Man in the Moon. But the view through a telescope, even at the lowest magnification, is more spectacular still. With huge craters filling the whole field of view, looking through a telescope at the Moon feels almost like being there.
In the early hours of 4 January, look out for more shooting stars than usual - possibly up to 100 an hour. It is the time of year when the earth encounters the stream of debris making up the Quadrantids meteor shower, and there have been good displays in recent years. Unfortunately, the Moon is full on 5 January, and so its light will interfere with the shower.
Venus, newcomer to the sky last month, is now a beautiful sight in the south-western sky, and by the end of January it sets three hours after the Sun. A telescope will show a gibbous phase, like an almost-full Moon. Mercury, too, puts in an appearance this month. During the first 10 days of January, it sets more than one-and-a-half hours after sunset. On 13 January, it is six moonwidths to the south of the red planet Mars. The only other planet worth looking for is Saturn, which is visible to the left of Venus this month, below the Square of Pegasus.
January Diary (all times GMT)
4 Earth at closest to Sun
4 4am: Maximum of Quadrantids meteor shower
5 8.51pm Full Moon
13 8.45pm Moon at Last Quarter
20 12.50pm New Moon
27 11.13am Moon at First Quarter
Heather Couper is also presenting 'Starwatch', a six-part series on Radio 4, every Saturday from 13 January. Between 5.40pm and 5.50pm, she will describe the view of the night sky from her rear terrace in Buckinghamshire, and then link live to an astronomical observatory somewhere else in the world. Destinations scheduled so far include the Hubble Space Telescope, the Anglo-Australian Observatory, and the SETI Institute in California - where scientists are searching for signals from extraterrestrial life.