Capacitor resistance measurement

So you mean, just apply the leads under the continuity test? That is really the only test to do with a DMM?
What happens is the DMM is charging the capacitor using a fixed (low) voltage through some internal resistance. As the voltage slowly builds up on the capacitor, the charging current decreases. It is actually not a resistance but electrical charge build-up on the capacitor. A certain time constant is associated with it, depending on the capacitance and the internal resistance of the DMM in this measuring mode. It is possible to measure the capacitance by measuring the charging time; some instruments measure capacitance on this principle.