If both compressor and condenser fan are not running, I would check for power to the outdoor unit first, and then see if the contactor is closed, since many units power up both the compressor and fan at the same time via the contactor. If the contactor isn't closed, I'd check the outdoor unit PCB for a flashing LED or other diagnostic telltales. Something is keeping it from engaging, possibly a low pressure cutout due to refrigerant loss.
HVAC units aren't really consumer-serviceable, so if you're unsure of what you're looking at it's best to call a pro. Safety first!