My normal way of checking, although lengthy, would follow the path of power from the battery to the motor checking everything is sound before moving onto the next step:
Assuming it is a brushed motor
1. Measure the voltage on the charger with a multimeter and check it is within specification limit.
2. Fully charge the battery.
2. Establish the input/output pin-outs on the battery connector and then measure the voltage across the output terminals. If the voltage is low, it would indicate something amiss inside. Check any fuses for continuity.
It could simply be a dry solder joint or a broken wire or some cells maybe faulty. I would not advise delving inside unless you have the knowledge to do so, it would be better to get it checked out by a qualified person.
3. While disconnected from the battery inspect the battery cable connector and cable for wear on the pins and if necessary remove the connector cover and check each wire joint on the connector.
4. Gain access to the controller circuit board and measure the voltage at the junction of the battery cable and the board after reconnecting the battery cable and switching on the key switch, be careful not to short anything out with the meter probes.
5. Check the switch wiring and cable for continuity.
6. With the drive wheel supported off the ground operate the throttle and the measure the voltage on the motor cable pins. If no voltage is present the the throttle could be faulty.
7. Obtain the throttle wiring diagram from the website and check all throttle connections and the cable is sound down to the control box. Locate the control signal wire from the throttle at its solder junction on the controller board and monitor the voltage across this point and 0v with a meter - it should vary as you twist the throttle.
8. Remove the motor cable junction box cover and measure the voltage on the cable wires. If not present then I would suspect a faulty controller. If present but the motor is still not running then remove the front wheel, remove the side cover and locate the brush holder and check that the bushes are not worn or sticking in the brush guides.