If you arrive in Santorini by cruise ship or you want to take a tour to the volcanic islands of Palaia Kameni, Nea Kameni and hot springs you have to move from Fira to the old port of Santorini which is located just below. The traditional way to get up and down is by riding on a donkey or a mule. The cost is about 8€ per person, per ride.
For those who are fit enough, there is always the option of walking up or down the 580 steps, following the same path with the donkeys.
The most convenient way to move from to the old port of Fira is to use the cable car of Santorini that takes only 3 minutes.