NSW has the biggest amount of taxis and taxi drivers in Australia. Sydney specifically has many cabs running around at all times. There are taxi ranks in very busy places in the city, airport and even suburban areas such as Bondi Junction. Where there aren't taxi ranks, you will often find taxis looking for passengers anyway.
The taxi services in Sydney are of several "brands" which unlike in other cities such as Melbourne means that our cabs aren't all yellow, and don't all look the same.If you get into a different looking cab today to what you did yesterday, it's nothing to worry about as long as the number plate has the official "TXXX" format. Remember, you can also ask to see the driver's taxi license. Some popular taxi brands include Taxis Combined, Silver Service, Premier Cabs, Legion Cabs and St George Cabs.
I don't know how taxi services in other cities work, but the "Taxi" sign on top of the taxi (depicted below), must be lit in order to know that it is available to pick up passengers. If you see an empty taxi, that is - one with the light on, as you may not be able to see passengers in the back, flag it down.
The sign is actually a light. When lit, the taxi is available.
Often taxis will try to check where you're going first through the window and have the door locked in case they don't want to take you. To avoid this, get in through the back seat, especially if you're in a crowded area such as the city.
At night, taxis cost considerably more in Sydney than during the day. Remember, if you know a faster way around your suburb than the driver, you can speak up and they can choose that route.
Taxis might be a bit more expensive than a bus or walking, but if you're going to the airport or even just getting home after a night out, it's a great idea to catch one just to be safe. Remember to stick the companies' numbers in your phone in case of emergency. You can also book online on their websites.
Here are the numbers for the companies I mentioned, if you feel like getting your phone out:
Taxis Combined 13 3300 Silver Service (02) 9020 9966
Premier Cabs 13 1017
Legion Cabs 13 1451
St George Cabs 13 2166