You've already made your choice, hired a rental car and you are on the road. If not, this article will help you before you sign a rental car contract: What you do need to keep in mind while picking up your rental car.
Here is some advice from me about the usage of your rental car. It will surely spare you a lot of trouble, nerves and cash.
What do I mean? Drive carefully and by the book. Do not drink alcohol before getting into your rental car. Avoid lending the rental car to others. Avoid using the rental car for towing other vehicles. Do not participate in street races. Choose routes on first class roads in good condition. Park the rental car on well lit parking lots with enough space around it for the pedestrians and the other cars and car drivers. All this will surely minimize the risk of any accidents and damage to the rental car - from small scratches to more serious accidents and damage.
If an accident occurs, do everything possible to save the rental car and control or minimize the damage to it. Inform the authorities as well as the rental car company as soon as possible. Fill out and gather all the necessary documentation about the incident, especially if it was not your fault.
In short - treat the rental car as if it is your own, because all damage inflicted to it while it was rented by you will be reduced from the money deposit you left when signing the rental car contract, especially if you can't prove, that it was somebody else's fault.