circuit diagram

The internal resistance of a voltmeter is usually very high (probably of order of Mega-ohms).
By [resistance comparable to that of the voltmeter] means that the resistor is of high resistance.

In such case, connect the resistor in series with an ammeter to a battery. Next connect a voltmeter in parallel across both the resistor and ammeter.

The ammeter measures the current through the resistor and voltmeter measures the voltage across the resistor (the voltage across the ammeter is negligible because of the high resistance of the resistor). Using Ohms Law, the resistance can be found by dividing the measured voltage by the measured current.