1. Look for an airfield that you own that has Available Transports (check tooltips or mouse over the airfield to show this information on top right corner)
2. Move your unit to this airport hexes
3. Next turn press Embark icon and move the plane.
That's because they're are very very very few instances of there being any transports available during campaign game play, there are more during specific scenarios bit those same scenarios being playing in their respective campaigns a lot of times don't have transports... It's kind of a bummer especially since it effectively makes paratroopers useless during the campaigns but during specific scenarios they're fun to use