Do you want to learn to program the Arduino? Divide your task into small steps, which you try out.
- Make your stepper motor work with the simplest stepper motor example code you can find
- Make your button work, like lighting the led on the Arduino while pushed
- Make a bit more complicated versions of #1 and #2
- Combine them, having your stepper motor react instead of the led
If that's not what you want to do, my guess is you don't actually want to learn to program the Arduino. And that's fine! Focus instead of having other people do the job for you. And prepare to pay for it. Following my list (or a similar to-do list) and running into problems may take you back here to ask more question. But at that point you have some code, some schematics and pictures to show us.