Whenever I visit my brothers and friends in California, I always drive their vehicles using only my Australian driver's license. Fortunately I have never had a collision while there, so I can't say for certain but let me explain my understanding. PS I was born in the US so I spent the first 15 years of my driving on California roads.
Vehicle registration should include some form of Third Party Insurance. You may then hear them use the terms 'comprehensive' or 'collision' when describing a policy. For example, my brother's truck is a 2001 so he only has it covered for collision. What this means is should I have an accident while driving it (or the same would apply if he was driving it himself) and the accident is MY fault, collision only covers to repair the other person's vehicle. Unlike in Australia where if you have an accident, irrespective of whose fault it is, normally your insurance company will pay to fix your vehicle and then if the other person was at fault they will try to recover from the other person's insurance company. In the US the insurance company of the party who is at fault normally pays to fix the vehicles. So if the vehicle you are driving is only covered by collision, and you have an accident that is your fault, the person who owns the vehicle you are driving may look to you for compensation to repair the vehicle.
It is my understanding that vehicles over 7 years old are the only ones which may have 'collision' policies so if you are driving a newer vehicle you should be certain it is covered by a comprehensive policy. Proof of insurance is mandatory, so generally there should be something kept in the glove box of the vehicle which shows insurance details. I do not believe there is any separate policy that you can take out yourself which would cover you to drive another person's vehicle. It is my understanding that an insurance policy for a vehicle covers any licensed driver, authorised by the registered owner to use the vehicle, but it may be best to have your friends confirm that with their insurance company.
I hope some of this helps. All of the above is based on California insurance rules so it is quite possible that there are variations in different states. One thing I can state for certain is DO NOT FOR ANY REASON take a US-registered vehicle out of the country (ie Canada or Mexico) as the insurance coverage will most likely be void.
