Most digital multimeters look like this:

1 = Display, 2 = Function switch, 3 = Transistor socket (optional), 4...6 = Test lead jacks

If you want to test a diode, set the function switch to "diode test".

Next, connect the test leads. Mulimeters usually come with two test leads: a black one and a red one. Connect the black test lead to the COM jack and the red lead to the V/Ω jack. Connect the other ends of the test leads across the diode. Connect the black wire to the cathode and red wire to the anode. The display should now read about 0.6V (600mV). If you swap the test leads, the display will indicate an overflow.

Note that in-circuit testing may lead to wrong results, since other components may be parallel-connected to the diode. Also make sure that the equipment-under-test has been turned off!