Read up on PWM to see some waveforms and how duty-cycle affects the waveform. The amount of time that the wave is "high" is the amount of time that voltage, and therefore current, will be applied to the LED. (or whatever device/component you are feeding)
Also, you can get a bunch of schematics on creating and using PWM with LEDs. A simple 555 timer and a few caps and resistors is all you need. Throw in a potentiometer, and you can change the duty-cycle in real-time. That way you can test your LED to "see" what brightness level you can accept.