Taxis are the easiest and most convenient way to get around Amman. They're ubiquitous and cheap. A trip clear across the city shouldn't cost more than 3-5JD, and most trips will cost less than 2JD. The base price is .250JD – always remember that there are 1000 fils in 1JD. Some unscrupulous cab drivers may try to convince you otherwise.
All cabs have meters, so make sure the driver turns it on. If they say its broken, get out and get another one. They will often charge double at night. Most of Amman's cabbies are friendly and happy to take you wherever you want to go. Also, it's expected that male riders take the front seat.
There are also white service taxis, which are shared and run fixed routes. They're cheaper than regular taxis, but also can be difficult for foreigners to figure out.