The coil works by lifting the ground, which causes the spark.
With key on it should have 12v(or 9v), at the "+" on the coil; with key in the Start position it should have 12v.
There are often 2 power sources for the coil, the Run power(key on) and the Start power, engine cranking.
The Run power comes from the key switch, and often runs through a ballast resistor to lower the voltage to 9v, this prevents the coil from overheating while driving.
The Start power comes from the Starter Solenoid, it either will have an "I" post on the solenoid or will be hooked to the starter motor side of the solenoid, this gives the coil the full 12v when cranking for a stronger spark.
The "-" side of the coil is where the points or ignition module is connected(also the tachometer), when this post is grounded(assuming power on the "+") the coil charges the secondary circuit, when ground is removed the secondary coil discharges a low amp high voltage "spark".
On the older systems the points opening and closing did the ground-no ground "firing of the coil"
On newer systems a transistor does this, based on a sensor in the distributor(pointless ignition) or a Crank and/or Cam position sensor(distributorless ignition).
But down to the brass tacks a coil still works the same way, power it then cut power and it sparks.
If you hook up a test light to the ground side of the coil and the "+" on the battery then light should come on and off when engine is cranking, with engine static it may or may not be a ground, depends on the system.
Electronic systems usually have the coil ungrounded when engine is static, this prevents heat up of the coils primary circuit.
I would check the "+" side of the coil to make sure it has power when cranking and with just the key on.