Physically determine unknown wire's gauge

http://www.zierick.com/pdf/wire.pdf

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This shows the stranded diameter and sub wire gauge+qty.

You can also measure the resistance of a meter of cable using 4-point (kelvin) connection (http://en.wikipedia.org/wiki/Four-terminal_sensing)

After that, you can use any online tool to obtain the AWG from the resistivity

Depends on how accurately you need to know. The most accurate would come from the geometry as described by Connor. For "close enough for bench work", I take a wire stripper that's always been fairly accurate, and see which set of notches strips the wire cleanly. For somewhere in between, I suggest carefully tinning a sample, applying heat well away from the solder so it wicks well into the strands without adding to the diameter, and measure with calipers.