Alright, let me just start with the statement that this is MY routine and does not mean that it's "The Best" way, just what has worked for me.
First off, there have been 2 general types of brake service that I've done, one is basically cleaning calipers and replacing with NEW brake pads. The other involves some type of disassembly of the brake system and changing/ flushing of brake fluid.
Either way, the basic steps are the same. I don't use MityVac's or Speedbleeders, just the old fashioned "pump and bleed" method.
The following are the steps I take. I work on one side at a time leaving the other caliper attached to the bike. I usually start on the Left side first, mostly because if the bike has an OEM type "over the fender" piggyback line the steps would warrant starting on the left first. For Race Lines that both go directly to the master cylinder, I don't know that it would matter.
1-Loosen the brake pad pin bolts. If the caliper uses "R" type clips on the pad pins, you can just wait until step 4 to remove the "R" clips.
2-Loosen the brake caliper mounting bolts and remove the caliper from the rotor without pushing the brake pads apart and pushing the brake pistons back.
3-While holding the caliper with your hand, pump the brake lever to close the gap between the brake pads. This will expose an obvious line from where the brake dust/dirt has built up on the pistons. You don't have to close the pads completely, just until enough of each piston has been exposed.
4-Remove the brake pad pin bolts ( "R" clips), remove the brake pads, and remove the Anti-rattle spring plates if they're still in place
5-Now take your favorite toothbrush and grab something to clean the calipers/pistons with. I know this is another area where everyone has their own favorite cleaner, I just don't suggest using any common type brake/ contact cleaner. I use Suzuki Bike Wash (comes in a 32oz. Black spray bottle with Blue label) that I cut down 50/50 into another 32oz. bottle with water. Also grab another spray bottle of plain water. The Suzuki Bike Wash works really well and won't hurt anything if you get overspray on the bike. Wash/ clean the caliper, pistons, pad pins, Anti-rattle spring plates thoroughly and rinse with plain water. Use compressed air to blow them dry and hold them with a towel behind them to keep from blowing the water all over......unless you have a nosey person who keeps getting in the way and is driving you nuts, then don't use the towel....whoa, where'd that come from??
6-Now comes the slightly more difficult part, but not too tough. Pushing the pistons back in. I only use my fingers.....waiting for it.........YES I CAN FIT MY FINGERS IN THERE....
now back to the subject, if I'm changing/ flushing fluid, here's where I put a clear hose on the bleeder, crack it open, and when I'm pushing the pistons back in carefully, I'm pushing the dirty, old brake fluid out of the caliper through the bleeder into the container. After I get the pistons retracted fully, then close the bleeder. If I'm changing/ flushing fluid, I also use a large syringe to pull the old fluid out of the master cylinder reservoir and dispose of it. Then clean/ wipe out the reservoir and add some fresh NEW brake fluid.
7-Now install the NEW brake pads, cleaned brake pad pins, Anti-rattle spring plates (if used) and install the caliper onto the fork mount. Install the brake caliper mounting bolts only finger tight, and also DON'T pump the brake lever.
8-Now go to the other side and repeat.
9-After both sides are done, calipers are installed with finger tightened bolts and reservoir is at least 1/2 full of fresh fluid......DON'T PUMP THE LEVER YET.... use the wooden handle of a hammer to tap from each caliper up the lines to the master cylinder and the banjo bolts. Watch the reservoir for any bubbles.
10-Now pump the brake lever to get pressure. Also at this point, bleed/ flush each side with your favorite method until you have clean/ clear fluid.
11-When you're finished flushing/ bleeding don't fill the reservoir. Just so it isn't too low.
Now here's my last step- I go back to the left caliper, loosen and take off the caliper mounting bolts one last time, lift the caliper off the mount but keeping it on the rotor. Then gently twist the caliper both ways to use the rotor to push the pads all the way back and the pistons all the way retracted. Do it gently and make sure that just the lid without the diaphragm/ bladder is loosely on the reservoir while you're twisting the caliper and forcing the fluid back up. Hopefully here is where you're catching any bubbles. Now install/ torque the caliper/ mounting bolts. Go to the other caliper and do the same thing again. Then install/ torque. Tap all the lines and banjo bolts with the hammer handle again before pumping the lever. Watch the reservoir for any bubbles.
Pump the lever to get pressure. Don't let the reservoir get too low. Fill the reservoir no more than 2/3 full with fresh NEW brake fluid when installing NEW brake pads.
Again, this is just my system that has worked for me. If it helps, great.