Start checking at the generator. Check the breakers on it, there should be 2.
Next is the transfer switch. Start the generator and listen for it to make a click sound as it switchs. That should happen in 20 to 30 seconds after startup.
If you hear the switch transfer, you have generator power.
Next is to open the transfer switch up ( with everything off ) and check the wires for loose or burnt connections or contacts. From there it's a straight shot to the breaker panel inside.
If no click noise, at the transfer switch, you will need to get a volt meter and see if the generator is producing power. If it is sending 120 volts to the transfer switch, it may have a bad activation coil or circuit board. You should be able to manually push the contactor, and make it transfer, with a insulated screwdriver. If holding it works, you need new parts in the switch.