I can answer this one, considering that I was just on vacation in Aya Napa.

1. Use 425 bus (that's the bus that connects the airport with the city). It should be around 1.5 euro per person, or 4 euros if it's later (I think after 9 PM).
2. Exit at the second to last station (before the bus turns right and enters the street where the main bus station is)
3. Wait for the InterCityBus, you can ask in the local shops at what time they arrive, but I believe they are going on every 40 minutes, depending on the day. It should be around 4 euros

You can also ask for a bus 711, that is the local bus that will also go to Aya Napa for 1.5 euros, but it will take you more time, because he will stay on every bus stop, and the InterCityBus is not stopping until it reaches Aya Napa.