On arriving at Corfu airport just go out to the taxi rank outside arrivals and take a taxi from there. There are usually several taxis available, just ask the driver to take you to the Sette Venti cafe at the new port. This is where all hydrofoils, boats & ferries depart from. It’s helpful to give them the name of your particular ferry boat or sea taxi.
The journey to the New Port will take about 10 minutes and cost between 10 and 15 Euros. At Cafe Sette Venti, there is a left luggage store there where you can put your bags in and wander into Corfu town if you have time.