LT3750 Capacitor Charger DONE pin
DONE is simply an open collector output that goes low when it is done charging:



The NPN transistor turns on when the output has reached the programmed voltage.  The pull-up resistor is needed to keep the signal high when the transistor is not turned on.

The DONE pin can only handle 1 mA of current through it's tiny NPN transistor, so unfortunately we can't use it to sink current into an LED directly.



A simple solution would be to use a P-Channel MOSFET (transistor) to drive an LED with the pin:







simulate this circuit &ndash; Schematic created using CircuitLab

The 100 kOhm resistor keeps the DONE pin high while it is charging, which also keeps the BSS84 transistor off.  Once DONE goes low, the BSS84 turns on and allows current to flow through the LED.

The BSS84 will work well for this.  Many others will work at 12 V as well, and will fully turn on.  

Now you just need to size your resistor for what LED you pick.

For example, if you choose a basic general purpose green LED (~2 V drop) and choose 10 mA of current to drive it with a 12 V VCC:

R = V/I = (12 - 2)/0.01 = 1 kOhm

This ignores the small drop across the transistor, but it can safely be ignored here as it is small and we don't care to get exactly 10 mA.