There’s one airport in Hong Kong (Hong Kong International Airport, airport code used by airlines/travel agents is HKG). There are many ways to get from the Airport to Sheraton, but the two easiest ways are:

1. Airport Express train then free connecting Shuttle Bus
Time: around an hour including waiting time (25/10 minutes train travel/waiting time and 9/20 minutes bus travel/waiting time)
Cost: HK$90 or around US$12 (or HK$160 if you buy a Round Trip ticket for the train)
Service Hours: 05:54 – 00:48 (train) and 06:12 – 23:12 (shuttle bus)
Details: The “Airport Express” is an airport/city connecting train. Take the Airport Express from the airport to “Kowloon” station, then take the free K4 connecting shuttle bus (show your Airport Express ticket or airline boarding pass before getting on). Sheraton is the first stop. If you are buying a Round Trip ticket, you must buy it at the service counter (the ticketing machines only sell Single Trip and Same Day Return tickets).
More details:
Airport Express:
Shuttle Bus:

2. Taxi
Time: 30-40 minutes depending on traffic
Cost: around HK$300 or around US$39
Details: Follow the signs in the departure hall to get to the Taxi terminal. Get on a red taxi (the other colored ones serve other areas of Hong Kong). Besides the base travel toll, you’ll also be charged extra for luggage handling and crossing the Tsing Ma Bridge. Taxis in Hong Kong only accept cash in Hong Kong dollars (they do not accept US dollars).

3. Bus
Time: around an hour
Cost: HK$33
Details: You can also take the A21 airport bus and get off at stop 14 “Middle Road, Nathan Road”.  It stops around 100 meters away from Sheraton, you’ll also need to cross a street.  You can find more details at  Input Route No > A21.  The site doesn’t let you direct link so you’ll have to click through all those to see the route.  It has a map and pictures of where the stops are.  Going back to the Airport would require going a little further from the hotel (stop 4 “New World Centre, Salisbury Road”).