What exactly is medium heat? Should I rely on the stovetop dial or is there a range of temperatures or the appearance of the item cooking that I should observe?
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Stoves vary a lot, and what's more there's a big difference between gas and electric, and even between different types of electric (induction or not). I've always looked more at the appearance of what I'm cooking -- high heat in a liquid is very rapid boiling, low heat is a simmer, while medium heat is a slower boil. It's harder for solid items - you can tell in an empty pan by putting a drop of water on an empty pan and watching its behavior (e.g. how fast it evaporates). This cool graphic from wikipedia shows the different behaviors at different temperatures: http://en.wikipedia.org...
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Please allow me to shout out loud that no two ovens or cooktops are calibrated equally---hey, try working with "gas marks" 1 thru 4 on European stoves! You can't just let it rip and walk away. Depending on what you are cooking an accurate instant read thermometer such as the Thermapen (which I highly endorse) can be a valuable tool. As far as appearance, are you simmering, boiling or braising? Each of these is a different thing. Are you poaching fish or braising meat? The term "medium" is next to meaningless.
Someone once taught me this trick... Put your hand over the pan about 2-3 inches above the surfance. If it's not warm at all, that's low. If it's warming your hand like a good fireplace but you can leave you're hand there, that's medium. And if you can't leave your hand there for more than a few seconds, that's high. Hope that helps!