By plane
By far the easiest way to get to Arequipa is by plane, landing in RodrÃguez Ballón airport IATA: AQP, 8km from the city. LanPerú (http://www.lan.com), Peruvian Airlines, Taca and Star Perú fly from Lima, Juliaca and Cuzco. A taxi from the airport to the Plaza de Armas costs a flat-rate of S/25. No public transportation available to/from the airport. Signs are posted with this rate, but depending on the size of the car, the size of your bags and your bartering skills you could pay less.
By train
Charter trains to Juliaca and Puno are only available for groups of 40 or more.
By bus
There are two terminals serving the city, Terminal Terrestre and Terminal Terrapuerto. They're next to each other, about 3km from the center.... a taxi should cost around 8 soles.
Try to avoid cheap buses — the more you pay the higher the quality, service, and safety. Some of the more reputable companies are Cruz del Sur, Ormeño, Excluciva full 180º beds with meals served, 130 Soles, Oltursa and Flores a good budget option. Their station is located across the street from Terminal Terrestre. If you take the night bus make sure the bus is climated. There are cheap companies like Julsa which don´t use heating in the bus and the temperature can sink close to zero - don´t use them. Compare prices between booking online, in the office or via an agency since it can vary up to 100% for exactly the same seat and service.
From Lima 30-130 soles, 16-18 hours it's advisable to take non-stop express buses — though more expensive, they tend to be safer. Oltursa and Excluciva buses depart from dedicated VIP terminals in the San Isidrio area of Lima.
There are several buses per day from Cuzco 9 hours, 50-120 soles, Puno 5-6 hours, 25-50 soles, Pisco 12-14 hours, 50-150 soles, Nazca 9 hours, 50-150 soles and Tacna near the border with Chile, 6-8 hours.
La Paz Ormeños has direct buses leaving at 1AM every day, passing through Puno at 6AM 40 Soles and arriving in La Paz at 12 midday 60$.