Is my stepper motor wired correctly?

Using Arduino Motors, Mechanics, Power and CNC
2

Sounds right to me.

If you need more current you should try to limit it to about 30 mA since the 40 mA spec is "Absolute Maximum".

The built-in Stepper library should work. Try File->Examples->Stepper->stepper_oneRevolution. You will have to change:

Stepper myStepper(stepsPerRevolution, 8,9,10,11);

to:

Stepper myStepper(stepsPerRevolution, 31,32,33,34);

If your stepper just hums or buzzes without moving, try swapping any two wires.