Basically the best way to see the city is to wander aimlessly around taking in everything; the smells, the sights and the people.
A must do is the short trip on 'The Peak Tram' which strangely takes you to The Peak. From here you get a fantastic view of the city and a look at the surrounding islands and harbours.
To avoid the pollution and rush of the city, take the short bus ride to Stanley. Here you have the market, the beach, and a shopping mall, as well as pubs and restaurants. The bus station is right next to the Star Ferry which is a must if you want to visit Kowloon.
There is so much to do in Hong Kong that you'll be kept busy for days, whether you want to shop on Kowloon or visit the smaller islands that make up Hong Kong, or whether you just want to sit in a cafe and watch the world go by...Hong Kong has everything for everyone.
Quick Tips:
The people are really helpful and most will speak English though some are reluctant to do so, particularly the bus drivers...so make sure you have a map with you so you know roughly where you want to get off.
Best Way To Get Around:
Walking is the best way but buses are cheap and simple. The major hotels offer free shuttle buses to various locations, including the shopping areas and the MTR (the Subway, which can be useful to avoid tired legs!).