What could be called the Sydney subway is Sydney's train system that does go underground, particularly in the city centre, but most of the time it's on the ground. Other underground train routes include sections of the line from the city centre to Sydney Airport.
In the city itself, the "Sydney subway" circuit is the City Circle whose underground city route starts above ground at Central in the southern part of the city centre, in the block bounded on three sides by Pitt St, Eddy Ave and Chalmers St.
From there it goes underground in two ways — think clockwise or counter-clockwise — passing the city train stations at Town Hall, Wynyard, Circular Quay (where it comes up for air), St James and Museum — in a circular route that brings the train back to Central.
If you hit Town Hall first, you're going clockwise; if Museum, counter-clockwise.
Where the city train stations are:
Wynyard: In the block bounded by George St, Margaret St, York St and Wynyard St/Regimental Square, close to Martin Place. Entrances at George St and York St.
St James: At the northern end of Hyde Park with main entrances on Elizabeth St at the end of Market St and on St James Rd either at the Hyde Park entrance or at Queens Square.
Museum: At the southern end of Hyde Park, with main entrances on Elizabeth St at the end of Bathurst St and at the junction of Liverpool St.
Don't ask for the subway. You may get directed to Subway, the foot-long sandwich roll place.