The public transportation system in Corfu and throughout the island is fairly well developed. There are two bus stations with public boarding points in the capital. The first station is located in San Rocco Square. Its Blue Bus buses, colored blue, are municipal buses. They can take you anywhere in Corfu Town and the nearest suburbs (Benitses, Dassia, Afra, Agios Ioannis, Achilleion, Pelekas). The traffic interval is 15-20 minutes.
The second station is located on I. Theotoki street (closer to the new port). This line of buses (Green Bus) is operated by KTEL. KTEL buses can be identified by their green color.
Buses connecting Corfu with other resorts of the island (Paleokastritsa, Kassiopi, Acharavi) depart from 1 to 10 times a day. The fare depends on the distance. Tickets can be bought at special kiosks or machines in San Rocco Square or from the driver, only in the second case the price will be 20-25% higher. In Corfu's public transportation, be sure to compost your tickets (they are valid for one trip).
You can find more information about bus routes in Corfu here.