Begin and end with the fiction
When players trigger a homefront move, ask how they do it. They Requisition the horses? Cool, who do they talk to and what's their pitch? They Muster the village? What does it look like? A town meeting? A speech at the public house? Or what?
Show the results of player moves in your descriptions, and in your portrayal of NPCs. The PCs Requisition the horses? Then describe folks hauling a cart themselves, glaring as the PCs leave town. A PC visits her sister after a Muster? Then portray the sister as tired and frazzled, and say how her shield and spear are by the door instead of hanging on the wall.
When the steading playbook changes, reflect those changes in the fiction, too. If Fortunes go up, describe the town's good mood. If you mark diminished, show how work isn't getting done. If Population goes up, discuss how the newcomers are settling in.
Show players how the game's mechanics change the village, and the village will feel dynamic and alive. Show players how their moves and their decisions affect the village, and they'll start to feel responsible for it.