Using a chef’s knife, cut around core and twist to separate halves. The core will remain stuck on one side.
Holding the side with the core in your off-hand, (gently) chop the knife into the core and twist to remove it from the avocado half. Reaching around the back side of the blade, pinch the core off with your fingers.
Scoop the avocado flesh from the skins using a large spoon, then slice/dice/mash as desired.
That’s how I learned to do it (in a tex-mex chain restaurant), anyway. I think maybe we were supposed to use one of those cut-proof gloves for step #2, but nobody bothered.