The exact process in the US can vary, but in short, there is a form used to document any existing damage to a vehicle before you start your rental. Basically, you do a walk-around (taking pictures can help) and if you note any damage, you bring it to the attention of a Hertz employee, either at the rental desk or exit booth. The employee then completes the form and documents the damage and has you review it and sign the form if you agree. Hertz takes a copy of the form and you keep the other two. When you return the car, give a copy of the form to the Hertz employee checking you in and keep the final copy for your records. In short, if there is pre-existing damage, as long as it is documented on a properly-completed form, you will not be liable for it after your rental.

If you drive off the lot without noticing damage or documenting it, you have very little recourse if Hertz decides to make a claim against you.