Dubai International Airport is around 2.5 miles from the city center and a taxi costs about $20 to downtown. Otherwise, the International Airport Bus is about 80 cents and goes to many hotels.
The Dubai Metro debuted in September 2009 and currently has 87 stations in many central locales. (And it’s continuing to expand). Otherwise, taxis can be hailed. In fact, if you hail a cab from a street, it’s cheaper than having a hotel get one for you.