This year the Eta Aquarids Meteor Shower is expected to be a great one, with up to 1 shooting star a minute at its peaks on the evening of May 6 and the morning of May 7 with no moon to interfere with viewing. Shooting stars from this shower will be visible from the April 19 to May 28.

Photo courtesy of Noriaki Tanaka @ Flickr
Dust from Halley's Comet
When comets pass around the sun, they leave behind a trail of dust which the Earth will pass through, resulting in a meteor shower as those specs of dust burn up in the Earth's atmosphere. For the Eta Aquarids it is the dust from the most famous comet of all, Halley's Comet.

Image of Halley's Comet courtesy of Professor Edward Emerson Barnard at Yerkes Observatory, in Williams Bay, Wisconsin.
Yes, I did say specs of dust. Your typical shooting star is just dust. Because the speed at which they enter the atmosphere, or more accurately, the speed at which the Earth's atmosphere runs into them, they burn very brightly. Should you see a fireball it will be a shooting star caused by something as large as a grain of sand.
Viewing the Eta Aquarids
Meteor showers are named after their radiant point, that is, where in the sky the shooting stars appear to be originating from. For the Eta Aquarids it is the star Eta Aquarii in the constellation Aquarius.

Image of the constellation Aquarius courtesy of Till Credner
To view a meteor shower it is not necessary to find the radiant point as the shooting stars will appear across the whole sky, however, if you do want to find Aquarius, then you can use an app on your phone or tablet. I use Sky Map, but there are many others. You can also go old school and get a manual star wheel as well.
The most important thing is just to get away from urban and suburban light pollution. Which usually means heading out to the countryside, though you might also try a beach, though. I know some people who head up mountains at night to view meteor showers.

Photo courtesy of Jason Jenkins @ Flicker
To be able to spot the shooting stars you need to acclimatise your eyes to the dark, which means no phones, smart watches, camera screens and definitely no flashlights. Also, while a campfire might keep you warm, its light will interfere with your viewing.
Find a nice place to sit, or better yet, lie down, and just watch the skies. At 1 shooting star per minute, it won't take long before you start to see them.
Viewing Times Around Australia
The general rule is that meteor showers are best viewed between the hours of midnight to dawn, with the ideal time in the hours before the first pre-dawn light starts to obscure the shooting stars: this is about half an hour before sunrise occurs, depending on how faint the shooting stars are.
With meteor showers, the 2 main obstacles to viewing are the weather and the moon. With the crescent moon setting early in the evening on May 6, the moon isn't even going to be an issue this year and I haven't included exact moonset times below. But if you are going out on other days to look for shooting stars, pay attention to when the moon will rise and set.
In
Sydney viewing starts at around 2 am with the ideal time to view this meteor shower will be between 5 and 6 am with sunrise at 6:34 am, while in
Melbourne, viewing starts around 2 am but peaks between 5:30 and 6:30 am, with the sun rising at 7:06 am.
Brisbane people should get a little earlier than the rest of the country, with viewing starting at 2 am, but ideal viewing between 4:45 am and 5:45 am and sunrise at 6:16 am.
Viewing in
Adelaide starts after 2: 30 an and is best between 5 and 6 am with sunrise at 6:56 am. Over in
Perth start viewing from 2 am with the ideal between 5:30 and 6:30 in the morning with sunrise at 6:52 am.
Photographing a Meteor Shower
Photographing shooting stars is a combination of good equipment, the right settings, patience and a great deal of luck. For the equipment, you will need a decent DSLR or mirrorless camera with a fast lens. Typical camera lenses have a lowest (that is fastest) setting of f3.5, which should be fine, but if you have a lens with a f2.8, f2.5 or lower, it will be much better.

Image courtesy of Amir shahcheraghian @ Wikimedia
Shooting stars move quickly so there is no way to point your camera at one to take the photo. Instead, you need to set your camera up on a tripod pointed at the sky and configure it to take continuous photos with the hope that you will capture one as it shoots past. Typical exposure lengths should be 10 to 30 seconds, with the longer the exposure the more of the star field you will see. But make the exposure too long the background stars will make it hard to see the shooting star.
Overall
This year the Eta Aquarids is likely to be well worth viewing because of the higher than normal rate of shooting stars and lack of an interfering moon.