It's a small block v8. The cap is the highest point in the system. There is a small overflow tank, 15 pound cap. What is the correct way to burp the system after changing the stat?

Well, a coolant recovery system will burp itself. Just make sure to fill the rad full first.
Now if you have a vent cap (the caps with the vent lever) you just flip the vent while its arm/hot and you will speed up the process.

You can then let it cool, come back when its cold and make sure the rad is full and there is still coolant in the recovery tank.

After I change a thermostat, I fill rad. back up to full level. Run it 'till it reached operating temp. Shut it off to cool back down. Remove rad. cap, add coolant if needed and put coolant in puke tank if applicable. I know some systems that I have owned require burping such as GM. If your system has a bleeder valve in line, then open bleeder valve while running. You will hear air hissing and then coolant should start spewing out. At that point shut off valve. You've purged the air from the system.

easiest is to drill a 1/32" hole in the flat of the stat just outside the center "mechanism" before installation. lets the air come thru so it will fill completely & does not affect cooling & only takes 1 minute to do. On a tough case with air pockets in the eng cooling passages, jack up the front of the car as high as you can & gun it several times with it warm (stat open)

and as you are filling, squeeze the upper hose like the docs squeeze a bulb to help people breathe. It will work some of those sticky bubbles loose.

Many newer cars have special procedures too. Mid-engine cars often require jacking and bleeders.
Toyota V6s require filling the heater hose, many FWD cars have bleeders too.

over the left shoulder, gently rub in a circular motion and pat firmly. i gotta come up with a new one, i use this everytime the question comes up.

Drilling a small hole in the thermostat works great.
You can also try using an aspirin, placed between the disc and the framework of the thermostat, install it and use your normal fill procedure..
The aspirin tablet will disolve rather within an hour or so, long enough to "Burp" out any air pockets.

When I do a fill on a smallblock I pull the heater hose off the intake and fill it till it pushes water out. Done this for some time and it works great with no problems.

Also did the hole in the thermostat thing as well.

Too late now, but you can fill eng through thermo opening with coolant until it is right at the mounting surface, then install thermo, install hose, top off rad and you're good.