Am I testing diodes properly?
In voltage mode, a multimeter just measures what voltage is present between its leads. What you want is diode test mode, which is usually indicated on the dial with a diode symbol. On your meter, it's the option one to the left of your voltage mode--set the dial to that and press the mode button a few times to put it in diode mode; it'll say on the LCD. In diode mode, the meter applies a known current to the diode -- you can check the meter's datasheet or instruction manual to know what current it uses, and fancier meters might even let you select a current -- and then measures the voltage across the diode.

Note that this usually won't work for LEDs, as most meters limit their diode test voltage to only one or two volts, which is too low to turn on any LEDs except maybe some red or yellow ones. But for a conventional diode like the one you show in the picture it will work fine.