Airline flights are very easy to find when planning a holiday in Amsterdam or Cyprus. Both of these locations see thousands of arrivals and departures each week, so you are sure to find a schedule that meets your needs and gives you the flexibility you want when on holiday. Amsterdam and Cyprus are served by most major international air carriers (British Airways, KLM, Lufthansa, American Airlines, Cyprus Airways, etc.) so you truly have a wide assortment of choices. Unless you absolutely must arrive or depart on a particular day or at a particular time, being somewhat open and flexible in your planning can often help you save a great deal of money on airline flights.
Whatever your final travel plans, it's critical to know the check-in policies and procedures for the airline(s) on which you travel as well as the security requirements and restrictions for the airport(s) from which you will arrive and depart.