How LEDs work
LEDs are not like standard incandescent (filament) bulbs in that they're directional. (Regular bulbs don't care which wire is + and which is - ). They operate much like a one-way valve for electrons. In the wrong direction they don't flow, and so they don't light. Unless you really over-power them in the reverse direction they don't suffer damage. In the right direction, they allow nearly unrestricted flow, which is good and bad.
LEDs are rated for a maximum voltage and current - current being flow and voltage being pressure. Too much of either is bad. Since LEDs can allow nearly unlimited flow when used in the correct direction, it is important that they be only given the correct amount of current, by using a resistor. This "current-limiting-resistor", or flow restriction, is like a kink in a garden hose. It reduces pressure and regulates flow. You can vary the amount of water leaving a garden hose by increasing or decreasing the kink in a hose with your hands, much like how a variable resistor (aka potentiometer) varies the current and voltage in a circuit. Unless there is a current-limiting resistor in the circuit, the LED will receive almost instant damage from the excessive current flowing through it. Similar damage will occur if the LED maximum voltage is exceeded.
LEDs typically want somewhere in the neighborhood of a few volts to light up. If you have 12v, and the resistor restricts the voltage to the appropriate amount, then you're in business. If not, and the resistor value is too small (the hose kink isn't restricting enough), the LED will be very BRIGHT for not too long. If the resistor value is too large (the hose kink is restricting too much), the LED will be dim for its life (which may be fine) if it lights at all. LEDs require a minimum voltage to work at all, so the resistor must be close for it to work. A good rule-of-thumb is that 12V applications require a 680ohm resistor. A good value for 5V is 330ohms. These values are good for people who just want it to work and are satisfied to see lights blinking for a while.
If you want to know for sure that the resistor you pick will work, this calculator will help. Try a supply voltage of 12V (like on the Ninja) and a forward voltage (voltage that the LED needs to work) of 2V. Now, say the LED wants 15 milliamps (a low amount of current; 1 milliamp is 0.001 amps, compared to the auxiliary circuit's fuse at 10 amps). The calculator is showing about 666 ohms, so that's close to 680. 680 is a "standard" value of resistors. So is 1 kiloohm (1000ohms), and this might be a "safer" resistor because it's going to limit current even more. If you punch in 12v and 2v again, but this time try 10mA (milliamp) you can see it comes out to 1000 ohms. That's also a "standard" value, and it will work ok too. The BEST thing to do is to put in correct values for the supply voltage, forward voltage and LED current. We know the supply voltage varies from ~12 to 14+ volts with rpm changes, etc..., so it's best to err to the side of lower current. So, using more than 12 volts as a value for a 12V vehicle system is necessary for the 'real world'.
LEDs have a direction. Here's how you can tell. In the symbol at bottom left, the triangle/vertical line is the symbol for any diode. The triangle points in the direction of current flow (anode to cathode), and the line represents the band found on the body of many diodes on the cathode side.
The anode (+ terminal) and cathode (- terminal) are shown with respect to the flat side of the plastic housing. The flat side corresponds to the cathode. If the LED is too small (very tiny surface mount components, for example) there won't be any physical shape to the LED, but there's usually some marking to indicate the cathode side, such as a dot or a notch.
Note that the anode is typically the longer of the two legs. Just be sure to include the resistor, as shown in the little picture in the calculator, and you're good to go. It can go either "in front" or "behind" the resistor, that is to say as long as it's in the circuit it doesn't care if it's on the + or - side of the LED.