How did you go school?

1. I went to school by my father's car.
2. My father drove me to school.
3. I went to school by car with my father.
[Which sentence is right?]

2 and 3 are correct.

1 would be correct if you wrote, "I went to school in my father's car."

If there's only supposed to be one answer, I'd say 2 is the best.

All three sentences convey the same meaning: you used your father's car to go school. Each sentence is grammatically correct, so you can choose any of them based on personal preference.