A driver is a human being and needs to rest. The Route Advisor tells you how long you driver may continue (lower right corner, "current order" tab - [F6] by default).
When a driver gets tired, special messages are displayed. You have to find a place to rest (marked with a blue bed icon). These are parking lots next to hotels or roads.
Park on such parking lot, turn off the engine ([E] by default) and go asleep ([Enter] by default). When you are resting you see only passing hours. Remember that you can rest when you are looking for orders but also during shipping cargo. Pay attention to delivery time as you may, quite literally, sleep through the deadline.
If you neglect messages remaining about taking a rest, the notifications will become more frequent, you will hear yawning sound and the picture will get darker with displayed "falling asleep" message. However, it does not limit your driving ability therefore you may continue and deliver the cargo.