If you want to sit back and enjoy the ride, a taxi is the easiest way for A to B transfers.
You can find a taxi rank just outside the Corfu Cruise ship terminal. Moreover, taxi drivers have a desk inside the buidling where you can get information about trips, transfers and prices.
For larger groups up to 8 persons, you will need a minivan. Corfu Taxi company has some minivans, and they can also be arranged locally.
For large groups over 9 people, a minibis Can be arranged through local travel agents.
You can find some taxi or a bus present upon your arrival at Corfu Port. However, booking in advance will give you the option to get the best quote for the route you are interested.
Ask for a private chauffeur if you are interested on luxurious service.
If you prefer maximum flexibility on your transportation around Corfu, you may consider to rent a Car at Corfu port.