Esfahan International Airport or Esfahan Shahid Beheshti (IATA: IFN) (ICAO: OIFM) was a military air base before the revolution. There are daily flights to Tehran and Mashhad in Iran. There are also flights to Damascus, Dubai and Kuwait and recently Istanbul.
There is a night-train to Tehran and everyday there is a train to Mashhad. There are not yet trains to Shiraz.
Esfahan is well-served by highways. There are automobile routes to capital Tehran, Kashan, Shiraz, Yazd and Ahvaz.
Esfahan is well connected to most parts of the country by bus . there are buses from Esfahan to Tehran and Tehran to Esfahan every 45 minutes. Also there are a few luxury buses with a so-called "European standard" (very comfortable seats, open mini-bar, etc.). "Royal Safar Iranian" is one of them, and don't forget to buy the 185,000 Rials (~$8) ticket to get the full package.
It is easy to get around Esfahan by bus, and possibly the cheapest way as well. A single journey costs 5000 rial; you can pay the driver directly, or buy multi-journey contactless cards at certain bus stop booths. Note that there are separate men (front) and women (rear) sections on each bus.
From Kaveh Bus Terminal, one can take Bus 91 which runs down Chahar Bagh-e Pa'in St towards the city centre, past Takhti Junction and Imam Hossein Sq.