Sydney's public transport network runs on a smartcard system called Opal (www.opal.com.au).
The card can be obtained (for free) and loaded with credit (minimum $10) at numerous newsagencies and convenience stores across Sydney. When commencing a journey you’ll need to touch the card to an electronic reader, which are located at the train station gates, near the doors of buses and light-rail carriages, and at the ferry wharves. You then need to touch a reader when you complete your journey so that the system can deduct the correct fare. You get a discount when transferring between services, and after a certain number of journeys in the week, and daily charges are capped at $15.80 ($2.70 on Sundays). Weekly charges are capped at $63.20. You can use the Opal card at the airport train stations, but none of the aforementioned bonuses apply.
You can still buy single tickets (Opal single trip tickets) from machines at train stations, ferry wharves and light-rail stops, or from bus drivers. These are more expensive than the same fare using the Opal card, so there's not much point unless you don't think you'll use $10 worth of transport during your Sydney stay.
You can purchase a child/youth Opal card for those aged four to 15 years; they travel for half price. For student and pensioner discount Opal cards, you have to apply online.
You can also use contactless credit/debit cards on train, light rail and ferry services, but you won't get discounts for off-peak travel or transfers.
389 Interesting bus route from Darling Harbour to Bondi Junction.
B1 Express bus from Wynyard to the Northern Beaches.
City Circle This loop of stations is handy for most attractions in the centre.
T1 The northbound train line that crosses the Harbour Bridge.
F1 The Manly ferry, a glorious half-hour cruise from Circular Quay.
F4 This picturesque ferry ride takes you to Watsons Bay via Rose Bay.
The line running from Circular Quay to Central down George Street opens in 2019 and will be great for above-ground city-hopping.
City Used by buses to refer to the CBD (Central Business District, ie downtown Sydney).
City Circle The loop that goes around the centre's main railway stations.
Light Rail The city's tram network, with two separate lines.
Opal Card The card used to access the city's public transport. Buy it from a newsagent or service desk, load it with money, then tap it on the reader when you start and finish your journey.
Opal Single Ticket If you don't have an Opal card, you can buy single tickets from machines in stations, but these are poor value.
Sydney Metro A new underground rail project, not yet operational.
Water taxis are a fast way to shunt around the harbour (Circular Quay to Watsons Bay in as little as 15 minutes). Companies will quote on any pick-up point within the harbour and the river, including private jetties, islands and other boats. All have a quote generator on their websites; you can add in extra cruise time for a bit of sightseeing. It's much better value for groups than singles or couples.