The northern horizon at 3:00 am ACDST as seen from Southern Australia (northern Australia is similar but Gemini and the radiant is higher in the sky) on Saturday December 14. The Geminid radiant is marked with a cross.
(click to embiggen).
The Geminids are unusual in that their parent body is 3200 Phaethon, an asteroid, rather than a comet. It is speculated though that Phaeton is actually a "gassed out" comet, and so the debris that makes up the Geminids may still be cometary particles.
The Geminids are a fairly reliable meteor shower and this year moonlight will not significantly interfere.
Unlike the Leonids, where there is a very narrow peak of high activity, the Geminids have a broad peak and will show good activity well before and after the peak, and on the day before and after.
The radiant doesn't rise until just before midnight (daylight saving time) in most of Australia, so you will still have to disturb your sleep for this one. Australians should see a meteor every two to three minutes under dark skies in the early morning of the 14th, between 2:00 am and 4:00 am local time. You can find predictions for your local site at the meteor flux estimator (choose 4 Geminids and date 13-14 December, don't forget to change the date to 2013).
The International Meteor Organisations Live Geminid report will be useful to follow the shower.
At 1.00 am in the morning AEDST (midnight, AEST) Castor (alpha Geminorum) is about two handspans above the horizon and 10 handspans to the left of due north. Pollux, the other twin, is less than a handspan to the left again. The radiant is just below Pollux.When you get up, allow at least 5 minutes for your eyes to adjust and become dark adapted (even if you have stumbled out of bed in the dark, here's some hints on dark adaption of your eyes so you can see meteors better) and be patient, it may be several minutes before you are rewarded with you first meteor, then a couple will come along in quick succession (a meteor every two minutes is an average, they won't turn up like a ticking clock but more or less randomly).
Choose a viewing spot where you can see a large swathe of sky without trees or buildings getting in the way, or with street lights getting in your eyes. The darker the spot the better (but do be sensible, don't choose a spot in an insalubrious park for example). While the radiant is where the meteors appear to originate from, most of the meteors will be seen away from the radiant, so don't fixate non the radiant, but keep your eye on a broad swath of sky roughly centred just above the radiant (as the radiant doesn't rise very high, looking exactly at the radiant will mean you miss some higher up).
A lawn chair or something similar will make your observing comfortable (or a picnic rug spread on the ground and a nice pillow), and having a Thermos of hot coffee, tea or chocolate to swig while watching will increase your comfort. Despite it being summer, make sure you have a jumper or something as the night can still get cold
Guides to taking meteor photos are here and here.
As well, Orion and the Hyades will be visible and bright Jupiter and Mars will be nearby. So it will be a quite nice morning for sky watching. Keep an eye out for satellites!