you have a bi-polar motor.
you need to use an h-bridge. you can make one, or you can buy one. there are dozens available.
buy one from adafruit or sparkfun.
BEFORE YOU BUY, make sure the site you buy from has a forum and a data sheet, wiring diagrams, instructions and a tutorial.
my advise is that you are going to spend a lot more for this than the cheapest one off e-bay. but, you are not buying hardware, you are buying knowledge. you are buying help, and the work of others to make it easy to use.
consider that you do not understand how the stepper works or why, and what is needed to make a circuit for it. would spending $20 on that knowledge be worth the investment in yourself ?
the problem with the current motor, and it is only a problem for your current learning curve, is that the motor really as two circuits, two coils. each one has to be powered, first positive on lead 1 and ground on lead 2, then it has to be powered positive on lead 2 and to ground on lead 1. so, you have to switch back and forth. then do the same on the other two leads with a separate circuit.
it is a large motor, do not throw it away. once you learn about steppers, it will be one you will need for power.