Flight to Paphos airport (Ryanair & Easyjet recently seem cheapest but others might have special deals on)
plenty of car hire centres at airport best to search for cheapest before leaving
taxis at airport about 40 euros
just 20 minutes along coast road to Peyia
Peyia is approxmately 13 kilometres from Paphos.

There are buses from Paphos Airport to Coral Bay and daily buses which run hourly from Coral Bay to Peyia Village and back. Also taxis in Coral Bay. Bus fares are cheap!!!