Stepper Driver from Old Scanner

You see that long IC on the bottom left of the image?
That's most likely the driver for the motor... google the part # to understand how it works (Datasheets)
You can then find the power pins, and the logic input pins. From there, you can either cut traces and modify the board, or pull that chip off and re-purpose it on your own circuit.
I do not recommend using the power supply on that board. It will be operating on mains voltage levels, and is a major safety issue with the exposed traces and parts.

 

No problem... when it's time to get messy, post some close-up pics of the board. Front and Back, as clear and straight as you can get. The guys on here use photo editing software to impose the front and back together to see where the traces go... but this is difficult with angled pictures.
Providing a part number on that IC can get you a lot of help as well.
I think the trickiest part of this build will be the power supply.
While it is possible to use the one on the board, we do not yet know how the circuit is designed, so instead of guessing and having random internet strangers tell you if it's safe or not, or how it works... just ignore it completely and put your own power to the part of the board you need. If you have someone local (Even visiting a hackerspace or makerspace) then you can look into keeping the built-in supply.
Regardless of built-in or external, you need to connect your own hardware to this board. You *must* have a 'common' between the board and your hardware. This is required so that the logic has something to reference to see if it's a 'High' or a 'Low' signal. This 'common' is almost always either negative, or ground.

Best of luck on your project. See how far you can get and ask as many questions as you want.