Hi Frodobagginz,
Welcome to CFC. To drop a paratrooper, the unit must be in a city and not have moved this turn. (note: if you move the unit by railroad only, it does not count as movement.) When you click on the paradrop command from the orders menu, your curser turns into a little parachute when over hexes you can drop on. When you move out of range, a little X appears over the parachute. You can drop on a hex free of enemy units and can move one hex or attack. You drop by left-clicking on the target hex or you can cancel the airdrop by clicking on the city the unit is in. Sorry, I don't remember the keyboard command, either.
Airplanes are not required for paratroops in Civ II. To transport a unit by air, you need an airfield in the launching city and an airfield in the receiving city, range is infinate, but subject to interception if enemy fighters are stationed anywhere along the flight path. Only one unit per airfield per turn can take off or land and the unit cannot move after landing. This is for ground units only, air units operate under their only rules, and, of course, ships cannot be airlifted. good luck.