LEDs run a certain voltage, for example a white LED is usually 3-3.7v, the actual voltage will depend on the drive current and the LED itself.
If a LED is given too much voltage, it will try to draw a lot more current then it is supposed to take, so that could burn out the LED.
For some of those larger LEDs, they have a few LEDs in series, think LEDs chained together one after another. This will cause the voltage the LEDs need to change. For example, if two LEDs are wired in series, then the voltage the whole chain needs is now double that of one LED.
If you have a power supply or some batteries, you could try different voltages until the LEDs light up. For example, start with 1 Li-ion battery and hook it up to just the LED. If it lights, then the forward voltage of the LED is around that of the battery voltage. If that doesn't work, try something with a slightly higher voltage. Keep stepping up the voltage until the LED lights, and that should be close to the forward voltage of the LED. A adjustable power supply would be best, but a chain of AA batteries or something could be a decent substantiated. Just add one more AA battery each time the LED doesn't light.
Someone please step in if that is a bad idea.
Once you get the battery voltage needed, you can plug the voltage of the battery into the equation I gave above, and figure out the resistor you need.
The resistor doesn't have to be exactly the value you calculate, lower resistance = more current = more light, higher is the opposite.