How can a DC18V ~ 36V LED driver work with DC3.6V LEDs without burning them out?
Your driver will output a fixed current through a string of LEDs. 

Since your LEDs are rated at 700mA @ 3.6V, this driver will indeed supply adequate current for the LEDs without burning them out.

How many LEDs you can put in series on a driver depends on the drivers voltage range, in this case 18 to 36V.

So you can attach 18/3.6 to 36/3.6 or 5 to 10 LEDs to this driver.







simulate this circuit &ndash; Schematic created using CircuitLab

With 10 LEDS the output from the driver will be around 36V. That voltage is divided across each LED, so no individual diode has more than their rated voltage. 

Or more accurately, when driven with 600mA each LED will generate a voltage across it, close to 3.6V, the total of those voltages will be what you measure at the output of the driver.

When you hooked up an LED directly to the 9V battery you vastly exceeded it's rated voltage and it went out with a flash of light. You basically fused it.