Being able to copy a trip is only a feature on Travefy Professional. You can duplicate a trip by simply going on your active itineraries page, choose the itinerary or proposal you wish to duplicate, and then press the Copy As button. Select whether you want the copy to be an Itinerary or Proposal, and the copy will appear in your active trips list.
Here is what will be copied from one trip to a new one:
Here is what is NOT copied:
Itinerary item tags