During the summer, I plan to rent a car in Calfornia, USA and do some roadtripping in the south-western part of the USA. I would also like a day trip to Mexico. Can I just drive through the border or isn't this possible at all? Do I need any special preparation?
This varies from Car Rental company to Car Rental company.
I've found someone who compiled the list of most major car rental companies and their policy w.r.t. to driving the car to Mexico.
Most don't allow it. Some do allow it with additional coverage for just such an occasion like Budget.
So if you know which car rental company you will be renting from you can look at their terms and conditions and get the real answer.
P.S. Technically though you could drive your rental car to Mexico and not tell anyone and border control will likely not bother you about it but would you really want to take the risk?
If a rental car is impounded, the owner of the car, which is the rental company, must show up in person to claim it. Since most rental companies don't have an agent in Mexico to claim the car this is a problem and the rental companies who don't have an agent won't give you permission to take the car into Mexico. You would likely be paying for the car while it is impounded and the rental company who does not have an agent is figuring out who can go to Mexico and get the car.
Many rental companies near the border area do allow their cars into Mexico.
You also need Mexican insurance. If you are certain that you are taking the car into Mexico and the days it will be in Mexico the car rental company will likely provide you insurance from a Mexican carrier. If you don't know when, they normally will tell you to stop and get it when you enter. Instant Mexico Auto Insurance often insures cars from International Car Rental when the people do not in advance know the days that they will be in Mexico.
I think it's impossible.
On the American side, rental agencies do no want their cars to be driven into Mexico in most cases. On the Mexican side, there is a law or ruling about importing cars that does not help either. Maybe it is best to park at the border, cross by foot then rent on the other side if necessary. Also, if you are a non-US resident, prepare to do the usual paperwork again for re-admission into the United States.