I think there is an easier way.
Firstly to not have to solder, buy a breadboard @ radioshack. You will also need some jumpers (little wires that can be plugged into the bread board and arduino sockets).
I think you should start a tad smaller. You can learn a lot about electronics in a single day, which will save you many days later on. First
Get a couple of LED's from radio shack, and a few resistors. (You might consider getting a getting started with arduino kit or other electronic kits)
Play around with making the arduino make the LED's blink then move on to motors.
Go through arduino's sample library and try to understand what is going on first. I was able to go through most of the tutorials in 1 day. After that I was very comfortable driving motors.
Another thing to consider... The arduino can only supply 1.5-2 amps (Im estimating but its very low), so it will not be able to power a medium sized stepper motor.
You will probably need a motor driver (http://www.radioshack.com/product/index.jsp?productId=12333768
I would recommend you start out with servo's then move up to motor drivers (servos are cheap, and can be powered without a motor driver)
I am happy to answer any other questions (within my knowledge) if the above does not help.
If you really want to jump straight to steppers:
1.) find out the amp draw of your stepper
2.) buy a motor driver capable of providing it adequate voltage and current
3.) connect the motor driver up to a breadboard, then connect the arduino up to the breadboard, and finally attach a jumper to connect the two to each other.
4.) Use this image and code: http://www.arduino.cc/en/Tutorial/StepperBipolar