Know how to drive safely. Learn basic automobile repair. Know about other regulations for automobile owners and operators.
Popular Mechanics recommends the following skills (and a few others; see http://www.popularmechanics.com/home/skills/4281414):
You should also know how to change oil.
In the event that you get in an accident, stay calm but check for injuries immediately. Even if the accident is minor, call the police and wait for them to arrive at the scene of the accident. You can find some more tips here: http://www.statefarm.com/insurance/claim-center/auto/what-to-do-after-an-auto-accident.asp.
Be sure to have your vehicle inspected regularly. Regulations vary by state, I believe, so you’ll need to check the relevant laws yourself. For example, in New York State (according to http://www.dmv.ny.gov/vehsafe.htm):
All vehicles registered in New York State must get a safety inspection and an emissions inspection every 12 months. Both inspections are also required when the ownership of a vehicle is transferred…Both inspections are done at the same time by a DMV-certified inspector at privately-owned inspection stations licensed by DMV.
When purchasing a vehicle, do your research and make sure you get a title transferred.