You should be able to work out an acceptable secondary voltage through a bit of analysis of what you have.
(1) What's connected directly to the secondary? A bridge rectifier? Then a voltage regulator, or some discrete parts?
See if you can reverse engineer this part of the board. Draw a little bit of a schematic out.
(2) Do you have a variable DC supply handy? Once you find where the DC gets made, you can try attaching your supply and slowly winding it up until the device comes to life.
(3) Other hints may be in the battery voltage (if the device can also be battery operated) and the max voltage ratings of the chips used on the board.
How can I know the + and - of the primary?
It's AC, it does not matter. Assuming they haven't done something silly like attach the core itself to one of those terminals.