Q:

How to capture unoccupied enemy-controlled territories?

How do I capture them? (besides tanks blitzing). That would not work if im trying to capture an island. Just move in with a bunch of infantry and claim it for myself?

A:

You can capture an unoccupied enemy terrority either by blitzing through it (as you mentioned in the question) or by moving a land unit into the territory.  It is treated as a combat move and is essentially as if you are fighting a battle against zero defenders (which you automatically win)

