The red cable on the right hand side with a black and white wire in it comes from the transformer. The smaller cable with two wires on the left hand side comes from the doorbell... I absolutely can't remember how this was wired when I took it out to paint the wall... Any clues, guys? Dudes?
Get a multimeter and test for ac voltage dc voltage and (with the transformer unplugged) continuity to see which are for the button.
Edit: actually you know which wires are the transformer. If the transformer is ac to ac, it doesn't matter which wire is positive vs negative for the bell. Our doorbell works like that.
If it's dc, then the red vs black does matter. There'd be labels on the wires inside the doorbell.