If you are visiting Sana'a getting around it shouldn't be so hard since there are a couple of ways in which you can do it.
Since it is a city which has kind of narrow streets in some parts of the city, there are minibuses that operate in Sana'a. They are very convenient and pretty cheap. They start running at 6 a.m until 1 a.m and are very commonly used by low-income workers. It would be best if you avoided traveling very early in the morning and very late in the night, especially if you are traveling alone. The buses are safe, but if you are noticed to be a tourist someone might try to pickpocket you. You may hear this buses also referred to as "dababs". You can hail a dubab by raising your hand when you see one approaching.
The best mean of transport in Sana'a are the taxis. The roads in Sana'a are pretty much like a labyrinth so a taxi would be a safe choice if you are afraid of getting lost. If you are traveling in larger groups they turn out to be quite cheap. The taxis in Sana'a are usually shared and these kinds of taxis can be found on the outskirts of the city the most. You can also grab a taxi to the surrounding cities (expect to Sa'da or Ma'rib). The taxis in Sana'a do not use a meter so make sure you agree on the price before setting off. In Sana'a, you will also see motorbike taxis which are pretty convenient especially in the Old City. They are fast and pretty cheap and can be found near any busy intersection.
If you are planning on using a car often, then it would be best to rent one then use taxis. The rental services usually will also give you a driver who will probably be bilingual. You will pay for the gas or for the number of hours depending on the package you purchased. If you decide to drive by yourself keep in mind that the drivers in Sana'a are usually aggressive. There are not may road signs so learn your path before setting off. Parking is also a little bit of a problem, especially in the center. Make sure that you park in a parking zone because the policemen are very efficient at handling parking tickets.