[jabl]

They made synfuels from coal, which contains a lot of, uh, coal. So no need to capture it from the air. They didn't worry about CO2 pollution back then.

[dredmorbius]

For fuel synthesis, you have two principle processes: carbon sourcing, and actually sythesizing the fuel.

Once you've got the coal sourced, most of the rest of the WWII process is directly applicable to modern carbon-capture methods.