A first point:
If you're looking into booking a holiday on Zante and you come across references to 'Zakynthos' don't worry. They're the same place!
While, of course, you might want to seek out a package holiday (using charter flights), the only scheduled flights from Belfast to the island are with Jet2 (They fly from Belfast International, not George Best, and ONLY ON WEDNESDAYS, from 4th May until 5th October).
http://www.jet2.com/
Flights are scheduled to take 4h 10m outbound and just 5 minutes longer coming back. Sample fares (at current prices):
Out on 11th May and back on 18th May = £169.20 return.
Out on 10th Aug and back on 17th Aug = £227.70 return.
The island isn't that big (roughly 25 miles by 12 miles), so a bus journey to anywhere won't take very long. The bus company's website is here:
http://ktel-zakynthos.gr/en/
There's only one official taxi company on the island. You can check fares and book here:
http://www.zantetaxi.gr/
(There are also some useful links at the top left of that page).
Wikitravel is, as always, well worth a read:
http://wikitravel.org/en/Zakynthos
Anything else, Conne?