Buy an Octopus card as everyone has said, which, if you don't have an onward boarding pass out of Hong Kong, will allow you to use the In-Town Checkin at Hong Kong Station (on the island) and maximise your day there.
I would recommend catching the Airport Express all the way into Hong Kong Station, then head straight out and walk down to the Star Ferry terminal, catching the upper deck to Tsim Sha Tsui and enjoying the view. At TST, walk to the Peninsula and have breakfast in the foyer, and enjoy the service. After breakfast, walk across the road to the HK art museum, and check out the fantastic collection of ceramics (there's a complimentary coat and bag check that will allow to browse unburdened). The collection of Chinese antiquities is great, and will cost $HK10. The gift shop in the museum is great for gift ideas. (It's closed one day of the week - check first).
If you've got space for morning tea, you can have a lavish morning tea at the Intercontinental 3 minutes' walk from the museum, right on the waterfront, which has one of the best views of Hong Kong (and therefore one of the best city views in Asia, in my humble opinion).
Catch the ferry back across to the island (using your Octopus card), and head into Central, the main shopping and business district. Look up to your right and notice the tall building near the waterfront with the large, round port-hole windows. Originally built for Jardines, the local Cantonese nickname is 'building of a 1000 coughholes'. For something different, pop into Shanghai Tang on Pedder St, which sells great womens wear, OK mens' stuff, and a great line of silk-lined books. Walk along Queens Rd Central until you hit the travelator, and catch it up to Hollywood Rd, and browse the antiques and homewares shops. Continue westward along Hollywood Rd and visit the Man Po temple, and have a look up some of the remaining 'ladder' streets that remain in the area.
By now you should be ready for a late-ish lunch. For something cheap and cheerful, you can try the lunch special at the Fringe Club on Ice House St (about $HK 80 for salad, bread, cheeses and the plate of the day), and whilst you're there, check out what art exhibitions are on in the complex. If you're hanging for a beer, the Fringe has a very casual roof-top beer garden. If you're into something more glam, grab a table at Isola in IFC2 (on top of the Hong Kong Station) which has a great lunch deal, with great views of the harbour.
Depending on what you want to do in the remainder of your afternoon, you could pop up to the Peak if the weather is good, walk around the zoo, or do more shopping. Worth a look whilst you're in Central is the iconic HSBC building (catch the escalators up to the banking hall and check out the atrium); very different in style, but very impressive is the public banking chamber in the nearby Bank of China. There are shopping malls all over Central, but the IFC2 mall and the Pacific Place mall (catch the MTR to Admiralty) are always good for a wander. The recently-opened Harvey Nics on Queens Rd Central is worth popping into.
If you have time in the evening, you can spend it in one of the bars with views in IFC2 (after having used the in-town check-in), then simply catch the lifts down to the rail platform, shower in the lounge, and board your plane. The best lounge is the Cathay First one immediately after Immigration (the Wing), and the adjacent Business lounge has chefs cooking up noodles to order.
