I used this guide for 1st Gen Mini first posted on The Mini Club of Ireland (miniclub.ie) with pictures, 2nd Gen Mini seats are similar but the wiring connectors are larger:
"I bought some, second hand half, leather cooper seats to replace my worn out cloth front seats on my R50 Mini One. "
Firstly you need to take the seats out of the car.
1: This will also involve disconnecting the seat belt pre-tensioner and seat airbags so make sure you turn the ignition off. (other guides also say to disconnect the battery and leave the car for 15 mins. I didn't do that and I didn't have any problems with my airbag warning light when I put the seats back in. You should probably disconnect the battery to be safe).
2: Look under the seat from the front, you will see a yellow (airbag) plug and a blue (seatbelt pre-tensioner) plug, unplug these by pressing the small tab in the middle of them and pull out.
3: Slide the seats back and using a T40 bit on your ratchet (for the 1st gen mini, not sure if this will be different for the 2nd gen), unscrew the front bolts. Once taken out, slide the seat forward and do the rear bolts.
You should now be able to lift out the seat.
(As long as you don't switch on ignition key while the seat wiring is disconnected there should be no airbag warning light to reset as no faults will be detected).