To be absolutely certain, you should:
* Consult your owner's manual: This is the best source of information for your specific vehicle.
* Check a repair manual specific to your 1989 Buick Century: These manuals usually have diagrams showing the location of all components.
* Search online for diagrams: A Google image search for "1989 Buick Century fuel filter location" might yield helpful images.
Be aware that working with fuel lines and filters requires caution. Always disconnect the battery's negative terminal before working near the fuel system to prevent sparks. If you're not comfortable performing this task yourself, take your vehicle to a qualified mechanic.