As requested by YamahaFan, Ive done the calipers myself, and documented it. This would be using a 1992 Kawasaki Ninja ZX-6D with two front 4-piston calipers.
First you will start off with a caliper looking something like this:
This is a typical brake caliper, in this case its a 4 piston (two on each side) caliper setup. My front brakes.
First thing you will want to do is make sure you have the correct tools and chemicals. Including:
Proper allen wrench to take the caliper off the rotor, and the proper wrench to take the caliper apart. Also a screwdriver to take the plate off the brake pads themselves, as well as to take the resivor top off. I use DOT4 Prestone Brake Fluid, brake cleaner, and a little bit of WD-40 in this process if things get messy.
And in this picture you will see a Syringe, and a cut in half water bottle, this is what i use to suck fluids, and/or add fluids to the main resivor. Not pictured at the moment is clear tubing i use when bleeding my brakes so I can see the color of the fluid coming out.
And the chemicals and brands I used:
Ok, now start off by taking the caliper off of the rotor using the main two screws that attack it to the front forks and examine your caliper and how you get the brake pads off. In this case its just two screws and a metal plate I take off. BUT DONT TAKE THE BRAKE PADS OFF YET
This next step will save you quite a bit of trouble if you do it before hand.
What you will want to do is put a rag between the brake pads and pump the brakes MAKING SURE YOU FINGERS ARE NOT IN THE WAY and make sure all the pistons are as far out as they come. Leaving the brake pads on allows you to adjust with a wooden tool (by simply sliding it between the brake pads and prying them apart) if your brake pads are coming out unevenly
Next you will remove the brake line from the caliper and make sure you hang on to the two metal washers on top and bottom like so:
And this is what it should look like after:
Now is the fun part. Make sure you have plenty of rags down on the ground, and around any painted objects or anything you dont want to get brake fluid on (the stuff is nasty!) And open the calipers through the four screws using your correct allen head wrench.
Your caliper should look something like this at this point:
Now you should be simply able to pry the pistons out of their socket with your hands, and if not you can use an air compressor to blow them out through the main inlet (but your brake caliper needs to be bled of fluid first, and put back together need be) So you should end up with something looking like this:
And as you can see... the inside of my calipers were very nasty. Sadly I didnt get an end shot of the inside cleaning, but its normally very shiny silver. And not the yellowish gunk you see now.
Now you basically just clean the inside of the caliper, and all around the piston until you get all the gunk and grime out. Use only a lint free cloth or cotton t-shirt and Q-tips to remove the gunk and grime. Liberally use brake cleaner on anything you need to get clean, this stuff works wonders and evaporates pretty fast after your done with it.
Also be very sure to make sure your o-rings and seals go back to where they were previously, and you MUST replace any orings that may have been damaged or fallen apart during the cleaning.
Now put the caliper back together like so:
Then replace the brake pads and brake pad metal cover plate.
After that, put the brake like back onto the caliper and make sure its the same way you had it before hand (pictures work very well if your not familiar with doing this!) Then mount the caliper back onto the rotor carefully replacing all screws.
Last step is to bleed the system making sure your resivor never runs dry so air dosent get back into the system
And there you have it! All done and you saved what a mechanic would have charged you $60+ along with anything extra he felt the need to add on.
And as a final side note: If your going to clean your calipers, make sure to do both of them if it applys to your bike, no point in only cleaning one side ^^ Want even brake pressure dont ya!
Ending Notes Added By Viewers:
First you will start off with a caliper looking something like this:

This is a typical brake caliper, in this case its a 4 piston (two on each side) caliper setup. My front brakes.
First thing you will want to do is make sure you have the correct tools and chemicals. Including:
Proper allen wrench to take the caliper off the rotor, and the proper wrench to take the caliper apart. Also a screwdriver to take the plate off the brake pads themselves, as well as to take the resivor top off. I use DOT4 Prestone Brake Fluid, brake cleaner, and a little bit of WD-40 in this process if things get messy.
And in this picture you will see a Syringe, and a cut in half water bottle, this is what i use to suck fluids, and/or add fluids to the main resivor. Not pictured at the moment is clear tubing i use when bleeding my brakes so I can see the color of the fluid coming out.

And the chemicals and brands I used:

Ok, now start off by taking the caliper off of the rotor using the main two screws that attack it to the front forks and examine your caliper and how you get the brake pads off. In this case its just two screws and a metal plate I take off. BUT DONT TAKE THE BRAKE PADS OFF YET

This next step will save you quite a bit of trouble if you do it before hand.
What you will want to do is put a rag between the brake pads and pump the brakes MAKING SURE YOU FINGERS ARE NOT IN THE WAY and make sure all the pistons are as far out as they come. Leaving the brake pads on allows you to adjust with a wooden tool (by simply sliding it between the brake pads and prying them apart) if your brake pads are coming out unevenly

Next you will remove the brake line from the caliper and make sure you hang on to the two metal washers on top and bottom like so:

And this is what it should look like after:

Now is the fun part. Make sure you have plenty of rags down on the ground, and around any painted objects or anything you dont want to get brake fluid on (the stuff is nasty!) And open the calipers through the four screws using your correct allen head wrench.
Your caliper should look something like this at this point:

Now you should be simply able to pry the pistons out of their socket with your hands, and if not you can use an air compressor to blow them out through the main inlet (but your brake caliper needs to be bled of fluid first, and put back together need be) So you should end up with something looking like this:

And as you can see... the inside of my calipers were very nasty. Sadly I didnt get an end shot of the inside cleaning, but its normally very shiny silver. And not the yellowish gunk you see now.

Now you basically just clean the inside of the caliper, and all around the piston until you get all the gunk and grime out. Use only a lint free cloth or cotton t-shirt and Q-tips to remove the gunk and grime. Liberally use brake cleaner on anything you need to get clean, this stuff works wonders and evaporates pretty fast after your done with it.
Also be very sure to make sure your o-rings and seals go back to where they were previously, and you MUST replace any orings that may have been damaged or fallen apart during the cleaning.
Now put the caliper back together like so:

Then replace the brake pads and brake pad metal cover plate.
After that, put the brake like back onto the caliper and make sure its the same way you had it before hand (pictures work very well if your not familiar with doing this!) Then mount the caliper back onto the rotor carefully replacing all screws.
Last step is to bleed the system making sure your resivor never runs dry so air dosent get back into the system

And there you have it! All done and you saved what a mechanic would have charged you $60+ along with anything extra he felt the need to add on.
And as a final side note: If your going to clean your calipers, make sure to do both of them if it applys to your bike, no point in only cleaning one side ^^ Want even brake pressure dont ya!
Ending Notes Added By Viewers:
If you have twin disc's on your bike, when you replace the pads, make certain that both sets of pads have the SAME batch code printed on the side of them. The first letter is dry braking code the second letter is wet braking code. Those are followed by the Batch Code. "You do want even braking don't you?"
Also, the higher the letters, the better the friction material used.
(think of them as buying diamonds only backwards.)