By taxi
Taxis ply the streets of Dubai and are relatively easy to spot. The easiest place to find them is at the taxi queue at one of the malls or outside a hotel. Waving down a taxi on the road is possible, but can be difficult during rush hours. At peak times (7-9AM & 4-7PM workdays, and Friday evenings) demand far exceeds supply, and not only are taxis hard to find, but those who deign to pick you up may demand crazy off-meter fares or refuse short rides in congested areas entirely. The standard of driving in Dubai ranges from poor to wild - taxis are some of the worst on the roads. Taxi drivers are pretty good at knowing where the main shopping malls and hotels are, however less well known places will mean the driver calling his brother-in-law to get directions, whilst he drives around in circles on your time - hence it is a good idea to have a rough idea of where you are heading or what a nearby landmark is.
Taxis are metered at 1.60 dhs/km, so no haggling is necessary. The rates of all taxi companies — Dubai Transport, National, Cars, Metro, and Arabian — are identical, so just take the first one that comes along. From the airport, there is a standing charge of 20 dhs; all other street pickups attract a standing charge of 3.00 dhs during the day, 3.50 at night (10 PM-6AM), but a minimum fare of 10 dhs applies, and there is a surcharge of 20 dhs for going to Sharjah. Taxis are exempt from the Salik road toll charges. Beware of unmarked hotel taxis and limousines though: while some of these are metered, they are not tied to the official rates, and can be much more expensive.
If you can't find one otherwise, you can attempt to call a taxi at 04-2080808, there's a surcharge of 3 dhs to book. The booking system was notorious for its unreliability but with a significantly increased taxi fleet, many taxis now deliberately wait in unofficial holding areas waiting for bookings. As a result, on a good day it can be possible to book a taxi and have it arrive within less than five minutes. If you absolutely have to get somewhere at a certain time (say, the airport or a meeting), it's still best to book a hotel taxi in advance, and get their estimate of how bad the traffic will be.
Women should travel in the back of the taxi as some drivers see it as an invitation if you get in the front.