The most important means of public transport in Jerusalem are busses. The bus network is extensive and every area of the city can be reached quickly. In addition there is the tram service, Jerusalem Light Rail. The trams pass about every ten minutes.
For longer journeys out of Jerusalem it is possible to take the train (e.g. Jerusalem – Tel Aviv takes around 140 minutes).
The Jerusalem public transport website is to be found here.
To get around the New City from Sunday to Friday there is a good bus service with two main hubs: the Central Bus Station in north Jerusalem and the railway station in south Jerusalem. On Saturdays (the Jewish Sabbath) Israeli buses do not run. However, if you are in the Old City, there are Arab Palestinian bus lines that serve nearby Arab villages.
Taxis can be hailed in the streets or booked by phone. For tourists there is a round tour bus (number 99) that allows you to hop on and off as it goes around the city.