The direction of electron flow will be from negative to positive. Many components of many appliances will not work if current is backward. Some can be damaged by reversed current.
If the applied polarity is wrong and there is no protection device like a diode, then the circuit burns up. If this is in connection with that board that has the four regulators on it, you can get the data sheet for any of them.
Using the data sheet as a guide and a meter to check, go from the unregulated voltage input pin of any regulator to the DC connector. Note which part of the connector is tied to the input, and you will see if it is center positive or negative.
UNLESS it's an audio device...things such as Boss pedals are set up for positive on the barrel, and Neg on the inner...they usually have a label there, though. Gotta watch that!!!