Most people reach for the channel locks or a big screw driver and bugger up the lip that holds the rubber boot on the caliper pistons . Usually you can pop one side out by blowing compressed air into the bleeder hole. To remove the other piston, take a medium hose clamp and tighten it around the piston, then pry on the edges of the hose clamp with a screw driver and walk the piston out.

It’s been a while but I’m pretty sure I’ve used a grease gun/pump also.

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That's it.

Watch the PMB video for a better way. They grind two vertical slots on either jaw of a vise and put the lip of the piston in that. It just wiggles out.

I have aluminum jaws on my vise, so they are soft enough to hold the lips without the slots. I just wiggled them off.

I use compressed air and a thin block of wood clamped to the side that had not piston.
Soaked in pbblaster if really rusted.

Rich

Brake fluid will pump through a grease gun. You’ll hate cleaning grease out of a rear caliper. I drilled and tapped a brake line fitting for a grease zerk. Piston pumps right out. Safer than air pressure.
If you hold the inner piston with a clamp and push the outer piston out with the grease gun you can rebuild one side at a time, or you can split the caliper and put a cap over the fluid transfer passages, bolt the caliper back together and pump out the outer piston.
I used a thin piece of aluminum with a little cardboard gasket.

My pistons had damaged dust boot “lips”, so I couldn’t grab the pistons in a vice. Plus they were stuck pretty tight.

That was my concern with the grease approach.

Given that you are going to replace the seals anyway it is OK to get destructive on getting the pistons loose so long as you don't scratch the pistons or bores. Sometimes heat is needed alternating with compressed air. Just make sure to take care when using high pressure air as the pistons will come out with a lot of force.

On my Lotus Elan that sat in a warehouse in Fallbrook since 1993 I had to cut a grove that allowed me to get a punch in to rotate the piston.

I have used the compressed air approach successfully. I totally agree that "the pistons will come out with a lot of force". Enough, in fact, to crack the front edge when they hit the other side. Get a good chunk of wood in there before, "quickly checking if this will work". Ask me how I know ...

Or just have PMB do it all and not deal with the mess