By flight
There are daily flights from Athens to the island. The airline companies that cover this route are the Olympic Air and the Aegean Airlines. The airport on the island is located very close to Corfu town and is easily reachable by taxi, buses or private vehicles. A bus connects the airport with the city, the price of the ticket is 1,50 € and you can buy it directly on the bus.
By ferry
There are two options for reaching Corfu from Igoumenitsa by ferry. You can either travel to the port at Lefkimmi or the one at Corfu town.
The port of Lefkimmi is located in the southern part of the island. The price of the ticket is € 7,10 per person and € 26,20 per car. It takes approximately 1 hour to reach the island.
This is the daily timetable: 8:00 – 11:00 – 13:00 – 15:00 – 16:30 – 18:00 – 21:00
The other port is located in Corfu town close to the city center. The price of the ticket is € 10 per person and € 40 per car. It takes approximately 1:30 h to reach the island.
There are different timetables for the busy season July 14 – August 30 and the rest of the year.
Timetable for July 14 – August 30:
2:30 – 3:30 – 4:30 – 7:30 – 8:30 – 9:30 – 10:30 – 11:30 – 12:30 – 13:00 – 14:30 – 15:15 – 16:00 17:00 – 18:30 – 19:15 – 20:30 – 21:15 – 23:30
Timetable for April 1 to July 14 & from August 30 to October 3:
2:30 – 4:00 – 7:30 – 8:30 – 9:40 – 11:15 – 12:15 – 14:30 – 15:00 – 16:00 – 17:00 – 18:30 – 19:15 – 20:00 21:15 – 23:30
If you are travelling by car my personal advice would be to take the ferry to Lefkimmi so that you have the chance to explore the island more thoroughly. I would also book accommodation outside of Corfu town so that I could feel the authentic atmosphere of the island, far from the crowds and the noise.