The pedal snapped off the crank arm and there is a portion of it left inside. How do I dig this out and replace the pedal?
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If there is a substantial length of axle sticking out of the crank the easiest approach is to remove the crank, grip the axle stub in a vice and turn the crank to unscrew it. You may also be able to use a vice-grip wrench instead of a bench vice. Remember that the left crank has a left hand thread.
If there is less axle sticking out: file a couple of parallel flats for an adjustable wrench. You might be able to use a Dremel or similar rotary tool to grind a slot for a large screwdriver.
If the above approaches do not work, the axle will have to be drilled out.
Steel pedal axles are far more robust than aluminum alloy crank arms, so hard to imagine the crank is not damaged also. If the pedal axle thread looks damaged at all, toss the crank - unless you want to attempt re-drilling and tapping it with a helicoil. If the crank is bent or cracked it needs to be replaced.