The Hunter wall mount control has two black wires and one green wire. How do I know which black wire goes to the black wire from the wall and which goes to the white wire from the wall? Or doesn't it matter which wire is connected to which

The green is your ground, screw it to the box back, The two blacks should never have any contact with the white, the white just passes through the box to the fan. The black from the box gets connected to one of the blacks on the switch and the other switch black goes to the fan. The switch just interrupts the black on its way to the fan.

The only way it will matter is if it is a remote control. If it doesn't work properly, swap the two black wires.