If you want to know the exact frequency, having a spectrum analyzer nearby while it is transmitting is probably the best way to find out the frequency on which it is transmitting. Failing this, a much less expensive option would be a frequency counter.
Knowing what frequency it is receiving could be calculated based on frequency on which it is transmitting and knowing the spacing according to the band plan and network technology.
If you just want to know the bands, either check the manual that came with the device, or do a web search on the device's model number.
Thanks,
Nic