1998 Lincoln Town Car O2 Sensors
There are a total of 4 O2 sensors on that car so without knowing which ones you have or are replacing they are located in two spots. The upstream/front O2 sensors are both located in front of the catalytic converters between the exhaust manifold flange and the converter body on each side of the engine. They could be very hard to remove so leverage can help. Disconnect the wire to them and then remove the sensor, reverse the process to put the new ones in, you will want to apply a light coat of anti-seize compound to the threads to aid in removing them if needed.
If they are the downstream/rear sensors the replacement process is the same except they will be located in the exhaust pipes following the converters on each side.
One very important item for working on this vehicle or any air ride equipped vehicle, is to turn off the air ride suspension before you try to lift it in any way other than a drive on style lift. There is a switch in the trunk area to do this, it is also the switch you would use if you had a flat tire and wanted to jack up one corner of the car. Failing to turn that switch off can cause failures in the air suspension system as it tries to correct for the height differences from lifting the car.
Suggested Repair
Do not assume both oxygen sensors are bad just because the scanner sets O2 codes; they can report a lean or rich condition caused by another fault. This car has four sensors: the upstream pair is ahead of each catalytic converter, between the exhaust manifold flange and the converter, and the downstream pair is in the exhaust pipes after the converters. Disconnect the wiring, remove the sensor (a special socket is optional), and lightly coat the new sensor threads with anti-seize. Before lifting the car, turn off the air-ride suspension with the trunk switch.
Conversation Summary
The owner of a 1998 Lincoln Town Car was told both oxygen sensors needed replacement and asked where they are and how to change them. The expert explained that O2 codes can be set by a lean or rich condition even when the sensors are working, and that the car has four sensors. Upstream sensors sit ahead of each converter; downstream sensors sit in the pipes after the converters. Replacement is the same either way: unplug, remove, and use anti-seize on the threads. The air-ride switch in the trunk must be turned off before lifting the vehicle.

