Shiraz International Airport (IATA: SYZ) (ICAO: OISS) has regular flights to all major and some smaller cities in Iran. There are International flights to Istanbul,Dubai, Sharjah,Kuwait, Doha.
Turkish Airlines is operating weekly 5 direct flights from Istanbul to Shiraz and vice versa.

By bus

Shiraz is well connected to most parts of the country by bus.

By car

Motorways connect the city to Isfahan, Kerman, Bushehr, Ahvaz and Yasouj, and Bandar-e Abbas is reachable by highway.

By Train

Shiraz Train station has recently been finished and there are Trains to Isfahan and Tehran. However, the bus journey is shorter (2hrs less), so that might be recommended

Get around
For non-Iranian visitors, taxis are probably the most convenient mean of transport. However be sure to haggle for a good price prior to getting into the car.
If an unmarked car stops while you are hailing a taxi, don't be alarmed. Many taxis in Shiraz are unmarked and also as a means to supplement their income, is not uncommon to find private car owners touting themselves as taxis.
However it always best to find a taxi through a reputable "telephone taxi" agency. For a set fee, drivers of these agencies will take passengers to their destination, drive them around town and also wait for them while they shop or run errands. All hotels and local residents will have a phone number of one these agencies. There are also taxis driven by women that specifically cater to women passengers.
The city also has a reasonable bus service.