Here is a link to a wikipedia article on bicycle brakes. Scroll down to the drum brake section. Click on the pic of the shimano drum (roller) brake for a nice enlargement.
The pic shows a rear brake, but the rigging is the same.
Bicycle brake systems - Wikipedia, the free encyclopedia
The cable jacket terminates on a fixed piece, that usually has a barrell adjustor.
The end of the cable moves the brake lever. Use the manufactured end of the cable in the hand lever.
If your Sturmey Archer brake did not come with a cable terminator for the "wheel" end (to pull the lever on the drum brake), make one with a nut and bolt squeezing the cable end, or you can buy something better from a hardware store.
Here's one of mine.