The distance from the airport to Corfu is 3 km. You can reach the town by the blue colored municipal buses #5 and #6 (the bus stop is located near the terminal building exit, the final stop is the central bus station). The ride to the city is only 10 minutes, just be aware that buses may be behind schedule.
You can also take the green-colored bus #19. The fare is 2,90 EUR. The final stop is Piazza San Rocco. The bus runs from 6:55 to 19:25, the interval is 1-1.5 hours, on Saturday - until 19:30 with the same interval.
You can also use cab services - the parking lot is located at the exit from the terminal. The price of a cab ride from the airport to the city is about 8-10 EUR (boarding - 5 EUR, 1 km - 1 EUR).