How can I determine which diffracted beam is +1 and which is -1 in the diffraction pattern formed by an acousto-optic modulator?
That is actually arbitrary. If the AOM uses a standing wave pattern, it is symmetric so you can call either first-order diffracted beam the +1 beam and call the other the -1 beam.
For a traveling-wave AOM, I would call the beams that diffract toward the direction of the acoustic wave propagation the + orders, but that's just my own convention. Those are the diffracted orders whose frequency is increased by multiples of the acoustic wave frequency.