Hi,
Buttons and the speaker will work fine connected either way. The LEDs (power and drive lights) won't work if the polarity is reversed, but it won't damage anything either -- you could just try it and turn the wires around if they don't light up.
If the polarity on the board or in the manual is indicated with "+" and/or "-", then the positive ("+") pin goes to the colored lead and the negative goes to the white (or sometimes black) lead. A dot or some other mark near one of the pins usually indicates positive.
However, as said above, nothing will blow up if you get it backwards and it will only make a difference for the LEDs. Don't stress about it too much.
