So how does one replace an oxygen sensor?

Pretty simple its in the exhaust so I would wait until cooled down, Locate them and use a wrench to remove it and same to install it, may have to use the electrical connector from the old one if you buy the one without the connector.

Threads directly into the exhaust and you see it sticking out from the exhaust with an electrical connection and wires coming from it.

Here below is a youtube video of the one in the exhaust manifold. Copy & paste it into browser.

https://www.youtube.com/watch?v=Z31b0v_zQ6s

There will be at least one more under the car just past the motor in the exhaust.

The Jaguar X Type is fitted with 4 O2 sensors one up-stream and one down-stream on each of Bank 1 and Bank 2 in line with OBDII requirements. So there you go you have 4 yes four oxygen sensors to replace.