1. Get an Octopus card - obtainable from any MTR station.  There is a cost incloved but the fares are then cheaper.  But it is worth it for the convenience.  Just wave the card and don't worry about finding the cost and having exact fare (change is not given on many forms of transport).  The cards are used on all transport, ferries, buses, the MTR and other rail lines.  Also many stores such as 7/11 and food outlets.  If only all cities had such a widely supported card.

2. The Star Ferry - The most famous public transport in Hong Kong is cheap and frequent.  But other ferries are also a great way to see more of the harbour.  One interesting island to visit is Cheung Chau, a half hour ferry trip from Central for $HK20.

3. The old trams rattle slowly across Central for $HK2.  Travelling from one end to the other, this is a great way to see life on the Island if not in a hurry. The tram is also useful for travelling just a couple of kilometres rather than walking along the miles of tunnels to get to the MTR.  For short trips the tram is quicker than catching the train, with much less walking.  One word of warning if you are tall - the roof on the tram is low and it can be a head-banging experience if you have to stand.

4. There are a few bus routes that are worth seeing too.  Route 973 travels from Tsim Sha Tsui, around Kowloon, crosses the harbour and winds around the coast of Hong Kong Island to Aberdeen, Repulse Bay and terminates at Stanley Market.  Up top the double decker bus this is a truly spectacular trip.  See WikiTravel for more bus routes and detailed instructions 
http://wikitravel.org/en/Hong_Kong#Se...