You can easily test all types of light bulbs with a device called a multimeter. Simple multimeters only measure amps, volts and ohms. To test LED bulbs, you need a multimeter with a diode setting. Look online or at your local hardware store for mid- to high-end multimeters that have this feature rather than cheap models.
For light bulbs, readings above zero indicate that your bulb is working, while readings at zero mean that the bulb has burned out and it is time for a new one. For fluorescent lamps, a reading between 0.5 and 1.2 ohms means your bulb has continuity and should work fine. For LEDs, a value of 3 ohms means your diode is working perfectly, an empty value means the diode is burnt out.