Adelaide has an extensive public bus network and is divided into three zones, and the fares are calculated according to the number of zones you travel.

The city center is in Zone 1 and the fare for this zone is A$1.60 (US$1.45/UK70p) from 9am to 3pm on weekdays and A$2.40 (US$2.15/£1.10) at other times. Kids always travel for half-price. Tickets can be bought either on board or at any of the larger newsdealers around the city.

Free bus (Source: eGuide Travel) 

Timetables and destination information can be obtained over phone or in person from the Adelaide Metro InfoCentre (Corner King William and Currie Streets | Open 8 am – 6 pm Monday to Friday, 9 am – 5 pm Saturday, 11 am – 4 pm Sunday | Tel. 08/8210 1000).

There's also a free City Loop bus (the one with no. 99C) which operates every 15 minutes (Mon-Thurs 8am-6pm; Fri 8am-9pm; Sat 8am-5pm) from around the city center and along North Terrace and many other stops.

Bus nos. 181 and 182 run from the city to North Adelaide.

The City Loop Bus. Adelaide. SA (Source: Amanda Slater) 

The Adelaide Explorer bus (Tel. 08/8293 2966) works extremely well with tourists as there it stops at as many as 26 important sights around the town. The ticket costs A$30 (US$27/£14) for adults, A$19 (US$17/£8.50) for children ages 6 to 16, and A$70 (US$63/£32) for families of four.

Tickets can be bought on the bus. However, if you are on a rush, this would not be a great choice. It is essentially a leisurely 3 hour loop, complete with commentary, and with hop-on and hop-off services. The loop starts at 38 King William St., on the corner of Rundle Mall (right next to the Haigh's Chocolates store) at 9am.

Equally flexible is the Adelaide Metro train system, with four main lines and two additional branch lines. The lines being:

• The Gawler Line, to Gawler Central in the north of the city.
   
• The Outer Harbor Line, along Le Fevre Peninsula in the north-west via Port Adelaide. There is an extension towards the beachside suburb of Grange.
   
• The Noarlunga Line, goes to Noarlunga Centre in the far south, via the beachside suburb of Brighton. An extension leads off to suburb of Tonsley. This extension works only in Mondays to Fridays during business and peak hours.
   
• The Belair Line extends to Belair, into the foothills of Adelaide Hills and to the south-east of the city.

The Outer Harbor line proves quite useful to get to Port Adelaide and even though the station is about 0.5 km south of the port, It is quite an easy walk up the Commercial Road.

Detailed schedule, and tickets can be fond here. Alternatively, tickets can also be bought on-board.

Adelaide suburban train (Source: Ruben Schade) 

The next options is to go for the tram service which runs along the Adelaide Entertainment Centre in Hindmarsh, and along the north-western suburbs, Adelaide CBD, North Terrace and King William Street, cutting across the city and onward to the south west before ending the route at the seaside suburb of Glenelg.

Tram travel within the city centre is free, and so is travel within the Jetty Road in Glenelg. Beyond that, the standard ticket system described for the buses apply. You can hop on to the trams at any of the stops and tickets can be bought from the conductor.

Adelaide Tram at Glenelg (Source: Ashley Kyd) 

Adelaide's train, tram and bus services are contracted and maintained by the State Government under the unified brand name of Adelaide Metro and uses a unified ticketing system called the "Metroticket".

The Adelaide Metro website or the Passenger Transport InfoCentre (corner of King William & Currie Streets, Adelaide CBD) provides timetables and route information.

There are a couple of choices for the tickets:

1. Single trip tickets ($4.40 for adults ($2.20 in off-peak)) Free travel around the transport network for 2 hrs. There's a "Multi-trip" ticket options which is essentially a combination of 10 single trip tickets.
    
2. Secondly, there's also a daytrip ticket. The pass costs A$7.70 (US$9.95/£3.50) for adults and A$3.80 (US$3.40/£1.70) for children 5 to 15. Passes can be obtained from train stations, local newsdealers, and the Adelaide Metro InfoCentre. This allows unlimited travel within the Adelaide Metro area for the day. 

Note: Tickets and route information can be bought from ticket machines on trains (coins only), or from the conductors on the tram or bus drivers.

Adelaide metro information (Source: eGuide Travel)