To book your trip for the move, either contact a travel agent (your company/employer might be able to recommend the one they use) or contact the airline directly (which often gives you better rates). Be prepared to wait if you call by phone at the busiest time of the day. Most tickets can be booked and purchased online (if you have a credit card), either on an airline's web site or a travel agent's web site. For air travel, e-tickets are increasingly common. All you need is your booking details and then you can check in directly at the airport, without a printed ticket.
There is an alternative: resort booking through a central reservation system, can ensure you the alternative and convenient facility of them booking your accomodation in their resort and booking the flights and all other arrangements for you under one or two invoices.