At rush hours 10AM-4PM, the best way of transport is on foot. Smoking is absolutely forbidden in all public transport ways.
By taxi
Taxis are plentiful in Damascus, making them a great mode of transportation. The taxis of Star Taxi, a new private company, are more expensive than normal taxis, but they are also more comfortable and safer. You can call their headquarters and they will send the nearest taxi to your door. Taxis with the Damascus Governorate logo on the side and a number on the roof sign are normally equipped with a meter, and it is best to use only these when hailing a taxi on the street. You should normally leave a 10-pound tip as well as the fare on the meter. At night, taxi drivers do not usually use the meter, so you may be best off negotiating the price before you get in. A service taxi to Amman or Beirut cost 700 Syrian pounds and takes around 4 hours and run 24 hours. Do not hesitate to take them; they are new, clean vehicles with air conditioning.
On foot
A very good idea is to go on foot especially for a sightseeing, and it's the only way to get around in Old Damascus. Walking in the new city however, should be reserved to the nicer areas of Maliki and Abu-Rumaneh, as the new city tends to be pollution clogged. The driving culture in Damascus is not the safest, so beware as a pedestrian, especially in the new city. Cars will not hesitate to come extremely close to pedestrians or other cars in order to pass.
Buses
Micro buses, also known as servees, are one of the main sources of transportation in Damascus. All journeys inside the city costs 10 Syrian Pounds 20 American Cents approximately. You can go from one place to another in Damascus with at most one or two journeys. When on the bus, give any passenger a coin and he will pass it to the driver and return the change, just remember to tell that passenger how many people you are paying for, whether you are in a group, or tell him that you are paying "for one" "waahid" if you are alone. The route is written in Arabic only on the roof sign. Micro buses do not generally have fixed stops except at very busy points, just beckon to the driver and he will stop near you Al yameen, andak iza samaht.
There are also many city buses that likewise cost 10 SYP. One useful bus is #15, which runs from Al-Marjeh Square Souq Sarouja\Old Town to the Western Bus Station, which serves Beirut and Amman.
By car
It isn't a very good idea to rent a car in Damascus. There is almost always a traffic jam, especially in summer, and parking tends to be difficult too; although that isn't the the situation in suburbs.