Normally, on the pcb board, there are little markings that tell you which is positive and negative. If you don’t see it, look at where the plug originally went in and find the place where one pin is different(via the underlying copper). If you can see where the other mounting pins went into the board(anywhere from two to six prongs) this will be your ground. You should see where the positive pin hits on a different line of copper, all together, and this will be your positive.
The way you can tell is get an electronic volt meter and set it to audible(this is usually marked with a sound or speaker icon) and test the points. Keep one tip on what you can tell is the ground and verify by touching another point that is the ground. If you hear a constant beep, that means these are linked to the same circuit. find the point that looks like it is on a different circuit and test it the same way. If you get no audible sound, that will most likely be your positive connection.
Without knowing exactly what kind of pcb you are working with, it would be ALMOST impossible to give you the right location.
Hope this helps.
Okay… Looking at your pics, the parallel hole furthest back from the edge of the board is your positive. The parallel hole closest to edge of the board and the adjacent hole is your common ground. Make sure to clean that board a little more before trying to solder it. thanks for the pics BTW!!