If you don't have your own car in Jordan, you're probably going to be riding a taxi. Public transportation in Amman here is limited and somewhat unscheduled, while privately operated buses tend to operate only on the most profitable routes. Biking and walking are rather dangerous due to a general lack of sidewalks and a Jordanian tendency to park on sidewalks that are available. Taxis, on the other hand, are literally everywhere. Unless you're on a side street or an an alley, there will be an empty taxi available within a few minutes. The exception is on Thursday during the evening rush hour. I've gone almost an hour without finding a taxi. The exception is on Thursday during the evening rush hour (basically the start of the Jordanian weekend). I've gone almost an hour without finding a taxi.
If you wanted to call a taxi to pick you up at a specific place, your only option is Moumayaz Taxi. Moumayaz is slightly more expensive than other taxis, but are the only company that takes fares by phone. They can be visually differentiated from all other taxis because they are silver rather than yellow. I've never had a reason to take a Moumayaz Taxi, because it's always been extremely easy for me to flag down a yellow cab instead.