You can go on an organised excursion which includes a coach trip of the island. If you're more adventurous you can do it yourself by getting a bus from Zante town. The bus timetable coincides with the ferry timetable. It takes about 75 minutes, so you'll have plenty of time to spend on Kefalonia. I want to travel flight-only.
Accommodation generally is fairly basic so look for features like a beachfront location or a pool.
Ignore the Tourist Office sign with the room rate and negotiate your own price. I always try to get transport first then look for somewhere to stay. It's much easier when you're mobile. They've got lots of information about hotels and apartments in the main resorts of the island. Try also the Zante Island Web Site made by Barry Coull , another Zante-crazy webmaster.