Connect your wires like this:
Red is your "load", or where the power is going to. Yellow is your "source", or where the power is coming from. As you can see in the pic, the switch is between these, able to cut the power on or off. This makes a full circuit.
The LED is outside this circuit. An LED needs power in (which it gets when the switch is "on", closing the circuit), but it also needs a ground. This is where your problem is. When you switched your wires earlier, you moved the ground from the the cc to the LED, or vice versa. You only had one in the circuit.
Evileks had his pic right, but his LED wouldn't work. If you leave connector 3 empty, your LED will not
work. Grab a piece of wire and ground connector 3 to something metal (your case, or a black wire from a spare molex connector) to include it in the circuit.
The "12 Volt" label on the switch just means it's a 12V switch, it's not for a particular connector.