It is almost always possible to find a good deal on a flight if you book early. From May to October there are many direct flights to Corfu from major European airports.
For groups and families an economic alternative to flying are ferries. For those who do not require much comfort, traveling on the deck of a ferry is an adventure in itself. Tip: bring a small pop-up tent on deck and throw your sleeping bag inside. Of course, you can book either a cabin or reserve a seat as well depending on your budget.
There are several routes from Italy to Greece. In the tourist season there are also direct routes to Corfu, but normally your first stop in Greece is Igoumenitsa. From Igoumenitsa there are hourly ferries to Corfu City or to Lefkimmi. The latter is better because the travel to Agios Georgios is shortest.