Almost no nation has all seven strategic resources at home. Trade is how you cover those gaps without invading anyone — at least until it suits you to invade them.
How Trade Works
Every country has a surplus of resources available to sell, and you can buy it by putting part of your civilian industrial capacity toward paying for it — the more you produce, the more room you have to import what you're missing. No prior diplomatic agreement is needed in most cases: basic trade is always available as long as there's peace and open routes.
Who to Trade With
Countries with large colonial territories or a lot of land tend to have big surpluses of several resources — think the United Kingdom, France or the USSR. Trading with neutral powers is also a common route for Axis or Allied nations that need resources their own allies don't have.
When Supply Gets Cut Off
Trade gets cut off if you go to war with whoever sells to you, if an embargo is imposed on you, or if your convoy routes get cut by the enemy. Relying too heavily on a single supplier for a critical resource is a risk: if that route gets cut mid-war, your production suffers right when you need it most.
Common Mistakes
The most common mistake is ignoring the trade screen for the whole game, letting your factory efficiency suffer from resources you could have bought with no effort. The second is relying on trade with a country you know you're going to attack later — plan alternatives before you cut the tap yourself.