How do I get a cleat that's stuck in a pedal, detached from the shoe, out? While out riding on my XC bike today, I encountered an issue with my cleat: The connector between the cleat and the shoe - the part that you screw into - died, and I lost a screw. So I had the shoe attached to the pedal, unable to unclip - because I was able to completely turn the shoe around without the cleat detaching. (The other cleat still worked, and I noticed that I couldn't unclip in a safe enough situation that I avoided biting the dust.)
When I got home, I detached the shoe my turning it around enough times that it unscrewed. (Trying to tighten it by screwing it the other way didn't work.) Unfortunately, now the shoe is detached, leaving the cleat itself still inside the pedal, with a single screw sticking out:

How do I get the cleat loose?
Your goal is to apply torque to the cleat as you would with your foot in a shoe.  So essentially you need something like a gigantic flat screwdriver.   I have a mini crowbar that would do the job, for example, but if you have any metal tyre levers they might be big enough.

Slacken off any tension adjusting screw first