Provided your fleet has sufficient movement, and loaded its invading ground units the turn before, it is not necessary to play the amphibious assault card to do an invasion.
Some terrain types cannot be invaded - snow is one of them - that is likely why your landing attempt near Narvik failed.
Axis units are normally tripled in defence against invading allies. This was done after playing games in which the Allies, with their large fleet, conducted numerous moderate-sized invasions from 1942, which was not historical and just didn't feel right. In an attempt to discourage that tactic, the Axis were given triple defence against amphibious assaults (it couldn't stop it happening but it made it less attractive).
However tripling units' against invasions raised the possibility that an Axis player who was doing well in the game and had sufficient forces to strongly garrison the coast, could make a Normandy-style invasion extremely difficult.
This is where the conduct amphibious assault card could be useful. For a major expenditure in political points (later in the war the Allies should have good PPs), and a pre-planning period of 6 months, playing this card multiple times will progressively lower the German defensive modifier to as little as 1.5 (thorough planning pays off). The cost can be shared between Britain, the US and the Commonwealth.
If the German coastal defenders are weak, you can save PPs and avoid playing the amphibious assault card at all.
The Rule book goes on at length (p. 35) about how this all works.
< Message edited by icym -- 3/12/2018 11:37:29 PM >