Dubai International is 5km from the city center.
Taxi - taxis are available 24/7 from ranks outside each terminal. They're cream colored and those with pink trim have female drivers. Many taxis have card readers. Some may accept US dollars, but it's best to have UAE dirhams on you if you want to pay cash.
Bus - while Dubai city operates a good fleet of modern buses, visitors tend to use taxis, which are good value. If you need to take a bus, they leave for various destinations in Dubai from stands opposite the terminals. Buses don't accept payment in cash, so to board you'll need to buy an Nol payment card in advance.
Metro - trains on the Red Line run around every 5-10 minutes from Terminals 1 and 3 between the airport and city center. Metro access can only be gained with a prepaid Nol card, which can be purchased from the station or from vending machines outside the terminal. Service only begins at 10am on Friday mornings.
Hotel shuttle - a few hotels offering a free shuttle service can be found near the terminals and in the airport free zone, as well as on the main Airport Road; these include Holiday Inn Express Dubai Airport and Premier Inn Dubai International Airport Hotel. The airport shuttle stop isn't well signposted and hotel shuttles often don't have a logo and just a display a small sign on the windshield - best to ask the hotel in advance for details.
Car rental - you'll find car rental kiosks in the Arrivals area at all 3 terminals.