The Sydney Harbour Bridge walk has been overshadowed by BridgeClimb, and these are two completely different things.
BridgeClimb is a commercial endeavour and involves climbing the top arch of Sydney Harbour Bridge. Walking across Sydney Harbour Bridge is free, and you take the pedestrian walkway on the eastern side of the Sydney Harbour Bridge roadway from The Rocks at the southern end of the bridge to Milsons Point at the northern end. Or start at Milsons Point and cross over the bridge to The Rocks.
You are not allowed to take your own pictures on your BridgeClimb. (They take the pictures, and you can buy what you like.) You can bring your camera and take terrific shots of the Sydney Opera House and other points of interest from the Sydney Harbour Bridge walkway.
Get a map
It's best to get a map from the Sydney Visitor Centre at The Rocks to find your access points to the Sydney Harbour Bridge walkway. Or ask at the centre for detailed instructions.
If you're in the Rocks area, you should find a sign along George St just south of Argyle St pointing you towards the long and sheltered flight of stairs leading to the bridge's southern end. These stairs are located near Gloucester St and Cumberland St.
The bridge can also be accessed from the south by getting on Cahill Walk, which runs along the Cahill Expressway above the Circular Quay train terminal. Pedestrians can access this walkway from Circular Quay by a flight of stairs, or a lift, or from the Sydney Royal Botanic Gardens.
Take your time
The Sydney Harbour Bridge Rocks-Milsons Point walk should take about half an hour with stops for picture taking. If starting at Circular Quay or the botanic gardens, the walk could take an extra 15 minutes to half an hour.
Take along a hat when the sun's out and wear appropriate clothes for the weather. Comfortable walking shoes are always a good idea.
If, on the other hand, you want to reach the topmost point of Sydney Harbour Bridge, there's BridgeClimb.