Front brakes:
If working on axle stands, chock the rear wheels - the handbrake may not hold.
Pads:
Check before you begin to see if you will need new caliper bolts. Some have stretch bolts which should not be reused. Make sure you have the torque settings to hand.
If the old ones have a wear sensor, keep the plug and wiring, don't throw it out with the pads. Joining the two wires will make a part you can use to fake the wear sensor if you get an aftermarket set of pads without one. (wear sensor is just a wire embedded in the pad, once it's worn through it lights the brake wear light)
Take the lid off the hydraulic reservoir. Leave the lid off while you do the job. Take some fluid out of the hydraulic reservoir to make room for what will be forced back as you push the pistons in to make room for the new pads.
Lever back on the old pads to force the pistons back into the calipers. That way the pads take care of any damage from the tools you're using to do the levering. In particular this protects the rubber dust seals between piston and caliper body. Lever the pistons back as far as they will go.
Check the new pads against the old ones to make sure they are the correct fitting, size and shape.
Clean off any rust and dirt accumulated on the pad guides. They don't need to be sparkling. Don't grease them - the pads don't move very far, and the grease will just stick more road dirt and brake dust to the guides than you would normally get. And you don't want grease near brake pads in any case.
If you haven't quite pushed the pistons in far enough, a pair of water pump pliers
like these can often be opened up wide enough to fit round the caliper.
Sometimes copper grease between the pad back and the pistons can
help with brake squeal.
Once new pads are in, (and new disks if you're doing them at the same time) pump the pistons back down gently until you get a solid brake pedal.
Disks.
The single countersunk securing screw may be rusted in. An impact screwdriver can
help to release it. Its main use is to keep the disk against the hub while you change a wheel - the wheel bolts take all the braking loads.
Rear brakes
If working on axle stands, chock the front wheels. Your handbrake won't
help once the wheels are off the ground.
Pads
As for the front, plus:
The rear calipers contain a mechanical handbrake mechanism which transmits force to the piston via a threaded rod which the piston is screwed onto. The mechanism adjusts automatically to keep the handbrake lever motion almost constant: the piston climbs up the rod, unscrewing itself a little bit every time the footbrake is applied.
To get the pistons back down and make room for the new pads, the pistons must be both forced back in and screwed onto the rods. A caliper windback tool from Halfords is a good way to make this easy.