Like other cities of Iran, in Isfahan you can use taxis and buses. Regarding rate, it's better to agree on a price before going on, whether for taxi or bus.
Airport Transfer: Isfahan airport is about 25km northeast of town, and as there is no bus service, you have to use taxi which cost around US$9.
Bus & Minibus: There are buses and minibuses leaving the terminal near Chehel Sotun Palace every few minutes with the cost of US$0.40 to US$0.90. Just remember to ask for the correct route for your selected destination.
You can pay the driver directly, or buy multi-journey bus cards at certain bus stop booths. Note that there are separate men (front) and women (rear) sections on buses in Iran.
Taxi: The rate is about US$2.70 to US$6.50 for private taxi inside the city. Chahar Bagh St. is the city's main thoroughfare and there are many shuttle taxis available for about US$0.10 per kilometer.