LED crash course:
LEDs glow when voltage is applied in the forward direction.
The LED has a forward voltage drop of about 2 V.
When feeding with 12 V, that means that 10 V will be over the resistor.
If the LED can handle 10 mA, this implies that the resistor should have 1000 Ohm (10/0.01) resistance.
Different LED have soemwhat different characteristics. But with the 1 kOhm resistor I suggest here, it will work. May not glow with the desired intensity, but it will work.
To make LED glow brighter you have to increase the current. But then they'll eventually add smoke to the menu. So to use, say, 50 mA instead of 10 mA, you'll have to pulse the current. 50 mA on for 1 ms, off for four ms, then 50 mA for another millisecond. The eye will remember the bright period across the blanking, and thus register the LED as brighter.
Again, the exact values depend on which LED you want to use. But without the current limiting resistor, it will either not glow at all (reverse direction) or burn immediately (forward direction). You can't even test it briefly without the resistor. If you have it correctly polarized, it will burn in no time.
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