To pop the pistons out stick a bunch of rags between the piston and the caliper. Get a blow gun with a rubber tipped nozzle and stick it up against the brake hose opening. Goggles on! Fingers out of the way of the piston because its coming out like a cannon ball. One little blast of air and it come out with a loud pop.
If there is more than one piston you need to block the hole of the piston you popped out so the air can blow out the other piston. I use to just stick piston back the bore just a little and clamp it with a large "C" clamp and then blow out the second piston.
The indie bore of the caliper never wears but the parts of the caliper that slide on the spindles do (It depends on the type of caliper mounting system) Take a look at where it slides and make sure it is not worn and its clean of all rust and dirt. Lube the slide area with disc brake caliper slide grease. If it cannot slide it is going to wear-out the outer pads
Stick the seal with the into the caliper. Its different than most seals. The square lip of the seal is designed to twist just a little as the piston extends outward. The twisted seal then helps pull the piston back in so the pad does not continually drag against the rotor.
You can either lube the piston and cylinder with brake fluid or brake assembly fluid which is a gooey slippery stuff that works better for installing the pistons. It helps the pistons slip past the seal. The next part is easier if done using two people. Somebody has to stretch the rubber boot with both hands far enough that the other person can stick piston into the boot. Then you need to square up the piston with the bore. Stick one of your old brake pads over the piston and with a big "C" clamp slowly pull the piston past the seal and into the bore.
When you go to bleed the brakes you can just gravity bleed them starting with the passenger caliper. Open the bleeder. Remove the master cylinder cap and gravity will do the rest. Just make sure the master cylinder reservoir does not run dry or you might be bleeding the master cylinder too.
Once the brake fluid starts flowing into the steel line any air in the line will be pushed ahead of the fluid and into the caliper. By the time the caliper fills up there is no way any air can be left in the line. I will see guys get in the car and stomp hard on the brakes a bunch of times before bleediing them. That causes any big air bubbles in the line to breakup into tiny bubbles that are harder to get out. If you do bleed the brakes using the two man system, open th bleeder starting furthest from the master cylinder and have the other person as slowl as possible push the pedal down once and hold it there. Close the bleeder and let the pedal back up. Repeat until no more air is coming out.
Easy on tightening the bleeder, it does not need to be gorilla tight. I see a lot of them broken off.
I just prefer the gravity method. Once I see the fluid trickling out of the bleeder I shut the bleeder and I'm done. Nice hard brake pedal every-time.
Brake fluid will eat your paint right off of your restored calipers.
I had to go Motorcraft brake school for the F-600 Girling hydraulic brakes when they first came-out, back around 1984. The factory Ford instructor made a good suggestion. He said, air bubbles will cling to the inside walls of a caliper just like they do in a glass of soda. He suggested tapping the sides of the calipers to break the bubbles so can flow up and out of the bleeder. It really speeds up the process. The trucks have big calipers.