* On the top of the transmission case: This is a common location. Look for a sensor with a single wire connector near where the transmission output shaft exits the transmission.
* On the side of the transmission case: Less common, but possible.
You'll need to consult a repair manual specific to your 1989 Buick Century (including the transmission type – 3-speed automatic, 4-speed automatic etc.) for the exact location and a diagram. A Haynes or Chilton manual would be very helpful. Looking up diagrams online via a parts website (like AutoZone or Advance Auto Parts) specific to your car's VIN may also help.
Caution: Always disconnect the negative battery terminal before working near any electrical components.