Damascus is a large city and has a variety of means of transports around it. That makes it easy to get around it. There are a number of transportations that you can use, just make sure that you have learned everything there is to know about the transportation that you are planning on using.
Renting a bike to help you get around Damascus is a great option. It offers a unique possibility to explore the whole city and the surrounding areas. If you decide to travel by bike, especially to the surroundings of the city, mak sure that you have an up-to-date map and bring lots of water.
In Damascus, you can find micro-buses, also known as servees, which are the most commonly used transportation. All the rides with these buses inside the city have a fixed price. To get from one to another end of the city, you will have to take one or two rides the most. When you get on the bus you need to pay the driver, just make sure that you tell him/her how many people you are paying for. The route is written on the top sign, but it is only in Arabic. These buses do not have specific stops, you just need to raise a hand at the driver and he will stop to pick you up. There are also city buses in Damascus which also have a fixed price and are very useful.
Renting a car in Damascus is not a really good idea because there are lots of traffic jams. Parking is also hard to find and the drivers are pretty aggressive.
There are a lot of taxis in Damascus and they are a good means of transport. The taxis of Star Taxi company are a little bit more expensive but more comfortable and safer. You can call them and they will get a taxi for you wherever you want. The taxis that have a Damascus Governorate logo on the side and a number of the roof usually use a meter and if you have to hail a taxi these are the best choice. However, at night they usually do not use the meter, so agree on price before setting off.