How can I spin an old HDD motor?

Most of the HDD motors are BLDC (brushless) motors. They can be driven by brushless ESC. Cheapest would be to buy hobby RC ESC and drive it by PWM. Something like this would be fine. (turnigy plush 25A).

25A means that it can be used to run motors up to that current without damaging ESC. You could find lower current ESC as well (but this one is cheap enough).

ESC consist of three wires, there are no 4 wires ESC. You need to measure resistance between pairs of wires and connect only wires with higher resistance. One with lower resistance leave unconnected.

I am not sure if I got your question correctly but I am assuming you are asking how to make the HDD motor spin continuously (also assuming you don't have a circuit in place to spin the motor yet).

AFAIK HDD motors are stepper motors with 3 coils to supply input source at different phases of rotation of the motor. You will need to provide it with a 3 phase supply voltage to work optimally.

I found a helpful schematic on the internet here. You could make your own driver circuit based off the schematics shown there.

Hope that I am not too late.

I wrote an article here. Basically I was using Arduino to send discrete signals to all 3 phases, but those three phases combine to give a continuous attractive force and make the rotor rotates. These signals allow the Darlington Transistors to pass a larger current to drive the motor.