http://www.measurementest.com/2010/08/how-to-measure-current-using-shunt.html

most cheap multimeters won't read more than 1amp before blowing an internal fuse.

that article explains putting a resistor in line will let you measure voltage and calculate the amount of draw.

I have a simpler article somewhere, but basically a 100 or 1000 ohm resistor lets you find the amps by just multiplying by 10 or 100 as I recall.