There's nothing different about Mini discs if you know anyone with a bit of car experience to lend a hand.
I'd remove the pads one at a time and press the pedal to push the piston a bit farther out so you can inspect & clean it - but you have to be careful not to eject the piston completely! They're designed for that not to happen if the pad is worn down to the metal to give you an idea. Large spanners make good levers for pushing the pistons back in, repeat until they move with barely no resistance at the pedal.
It's not a bad idea to use it as an opportunity to draw fresh fluid in to the caliper, but be wary the bleed screws can seize if they haven't been touched in a while and will be a much bigger job if you shear one. Proceed with caution if you need the car roadworthy. (and keep an eye on the fluid reservoir for topping up, with the same specification of fluid - usually Dot4)
Also, while you've got the wheels off inject some grease in the suspension joints - you will need a grease gun if you're going to be a Mini's domestic servant.