See Cronulla and Royal National Park for information on how to access those areas, and the information with the attractions on how to access them.
By bus
There are bus (http://www.131500.info) connections to Miranda direct from Hurstville and from Rockdale. Both are slower and more expensive than the train.
By train
Cityrail (http://www.cityrail.info) runs trains to the district every 15-30 minutes. The journey takes around 30-45 minutes. There are 13 Cityrail stations within the Sutherland Shire district.
The city train stations of Central, Town Hall, Martin Place and Kings Cross offer a direct service. From the other city stations you will need to change at Central to platform 25.
From Sydney airport change at Wolli Creek station.
By car
From the north there are three bridges over the Georges River that link to the Sutherland Shire. If you follow the Princes Highway south from the Sydney CBD towards Wollongong, you will enter the Sutherland Shire crossing the river at the Tom Ugly's Bridge. The journey will take around 30 minutes. Alternatively, you could travel along Rocky Point Road and cross Captain Cook bridge to enter the shire through Taren Point.
From the south Wollongong just follow the signs to Sydney via the Sydney freeway, and as soon as you seen the "Welcome to Sydney" sign, you have made it. The journey takes around 30 minutes but can be congested at peak times.
By bike
The cycleway from Sydney Olympic Park follows the Cooks River to the edge of Botany Bay through Southern Sydney. It enters the Sutherland Shire over the Captain Cook bridge and continues largely off-road or on quiet roads to Cronulla. It then continues on a wide shoulder on a 80km/hr road to Kurnell. Sydney cycle routes are generally not well marked, and you should do some research on the route and take a map so you don't get lost or end up on a very busy road. Sharkbike (http://www.sharkbike.org.au) is the Sutherland Shire Bicycle User Group.