My father drives the same car as Mr. Kimura.

Literal

Father [topic-は] Kimura-teacher [possessive-の] [same-と同じ] car [to-に] riding.

~と同じ means 'the same as.' 木村先生のと is an elliptical construction — 木村先生の(車)と同じ車, with the first 車 omitted.