Fly to Paphos international Airport.
Flights available with BA, Thomas Cook or First Choice and now Easyjet and many other flights can be found.
Kato Paphos is aprox 10km from the airport and will take about a 15 minute drive.
Car hire is available at the airport if required, although I would recommend to pre-book one and get a better deal(I found europe car the best on the internet).
A taxi from the airport should cost between 25-30 euros and I can recommend Stevies Taxis highly.
Car hire is not necessary within Paphos but it will be required if you want to explore the rest of the island