THey conduct in one direction, with a consistent difference in voltage. The voltage between the terminals for a silicon diode is about 0.6V, for a germanium diode is about 0.3V, and for LEDs is 1.2 to 1.4 or more, depending on the substance from which is is made. Then use your meter in current mode putting the diode in series with everything else, so you have a lopp consiting of the meter, the voltage source, the resistor and the diode. In looking in a manual I see that a 50V 1A diode has a 10 microamp current when reverse-biased, at rated voltage. That one is rated at a maximum of 200 microamps reverse-biased.
Diodes have two failure modes.
In the other, the junction separates, and they become a non-conductor. But it is necessary to be sure that you have sufficient voltage to forward-bias the diode.