As far as spectacular celestial displays go, comets are notoriously hit and miss. When astronomers began tracking comet ISON (pictured above in this Hubble Telescope image) following its discovery by Russians Vitali Nevski and Artyon Novichonok in September 2012 hopes were high that it would really light up the night sky as it rushed toward a late November rendezvous with the Sun before sling-shotting outward again to the far reaches of the solar system.
“Comet of the century” is how astronomers initially described ISON, and speculated it could reach the brightness of the full moon as it passed within 1.16 million km of the Sun on Nov. 28. Since then, expectations have been downgraded as the comet appears to be in danger of possibly disintegrating. Still, it could reach the brightness of the planet Venus, which should provide a reasonably impressive display.
To help orientate you in your search, the comet spent October passing through the constellation Leo, and in November it will sweep past the bright star Spica in the constellation Virgo. Your best bet for seeing the comet in the next few weeks is in the south-east before sunrise. Saturn, Mars, the Moon and Jupiter will also be in that area of the sky so there will be no shortage of stuff to observe.
Assuming the comet survives its close approach with the Sun it will remain visible until early January. You can find more detailed observation information here.