What's the best way to physically clean my monitor?

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The Tiger
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1. Unplug your monitor from the power, as well as the signal cable from the computer.
2. Moisten (not dripping) a soft piece of lint-free cloth with Isopropyl Alcohol (rubbing alcohol). You can use pure ethanol (70%) but I prefer isopropyl alcohol because of its quick drying properties.
3. Softly rub the display with the cloth.

Warning: Never apply much pressure to anywhere, where a stubborn thing is stuck. You might kill the pixels of your display, resulting in stuck or dead pixels. Rub repeatedly over the place, but never hard.