To measure the current that the motor is drawing in normal use, see this tutorial: http://learn.adafruit.com/multimeters/current
To measure the stall current (worst case current draw), just measure the resistance across the motor terminals and apply Ohm's Law. (I = V/R)
For example, if the resistance is 10 ohms and the supply voltage is 12v, the stall current is 12/10A or 1.2A which would toast the L293 chip on your shield. That assumes that your 12v supply is capable of delivering 1.2A. If it can't, the voltage will drop or the supply will shut-down.
The good news is that with your 500mA wall-wart, you probably won't be able to exceed the 600mA rating of the shield.