One adrenalin-inducing way to get across town in a hurry is on a motorcycle taxi. You’ll see them loitering on corners all over town, though the corner of Jomhuri-ye Eslami Ave and Ferdosi St is a good place to look for one going north. They cost as much as taxis but take half the time. Good luck!
Buses normally travel from one local bus terminal to another, so you may need to take more than one. Major bus departure points you might use include Imam Khomeini Sq, from where buses go in all directions; the terminal on the opposite side of Imam Khomeini Ave from the National Museum of Iran, for the west; Arzhantin, Vanak and Valiasr Sqs, for the north; Azadi Sq, for further west; and Rah-Ahan Sq, for the far south.
Buses never show their destinations in English and numbering is inconsistent. However, if you ask at the station or bus stop, you’ll be pointed to the right bus. Some handy routes going north–south include Arzhantin Sq to Tajrish Sq; Imam Khomeini Sq to Arzhantin Sq; Imam Khomeini Sq to Tajrish Sq; and Valiasr Sq to Tajrish Sq.
Private bus companies began operating in 2006, with newer, more comfortable and faster buses for a flat IR1000 cash fare. Azadi Sq to Tajrish was the first route, and expect more.