I drive but do not own an automobile. If I rent or borrow a car am I insured by owner's insurance?

If you "rent" from a car rental company they have insurance on the car but hold you liable unless you purchase additional insurance at the rental.

If you are talking about renting or borrowing another person car, it will depend, some policies are listed drivers only, others will cover any insured driver for temp use.

If you were going to be a full time driver, the insurance expects you to be a listed driver so the payment for insurance will be the right amount for the person driving