Aegean airlines (the link that Georgo has already gave u guys) is what i use to travel around Greece, and i travel a lot around Greece lately. That e-ticket u can get there is the cheapest way to travel by air, as far as i know, and from my job, im supposed to know
If ure lucky, u can get a ticket, from about 40 or 50 euros per direction, however, its not for Zakynthos, still it covers most of the major greek destinations. And yes, dont worry, it is a perfectly descent company, not anything like a cheap charter airline or something.
Still, another airticket link that might prove to be useful, is this: http://www.airtickets.gr. Good luck!
And Tim, Vasilipepe said it all about ways to get to/from Athens airport. I wouldnt worry too much if i were u or anybody else contacting us here, Greeks love their cars way too much and the road to/from the airport is the best in Greece, who doesnt wanna drive it? :D