how to measure the internal resistance of a voltmeter?
Apply a known voltage over a series resistor. This resistor in combination with the internal resistance will form a voltage divider. Say you apply 5V over a 1M series resistor, and the DMM shows it as 2.5V, then the internal resistance is 1M.  

edit
Now that I reread it, I guess it's not completely unambiguous. By "applying a voltage over a series resistor" I meant you connect the + to the resistor and the - to the ref. input of the DMM.