If you drive a vehicle for work, you check it before you set off.
Who checks? Usually the driver: before the shift, that the controls and safety equipment work, and during the journey, that no obvious defects appear. That applies to trucks just as much as to vans and company cars.
What if something is wrong? Report it to the person in charge straight away. If safety is at risk, for example brakes, steering or tyres, the vehicle stays off the road.
Does it need to be written down? That depends on the rules you work under. After an accident, though, it helps to show that the vehicle was checked. A completed list with date and name is the simplest proof.
Not legal advice. The rules of your country, your insurer and the vehicle's manual take precedence.