Update: Make sure to see the new post on this topic, containing a better circuit.

Some ICs, like the 555 timer, are able to source enough current to drive an LED. However many aren’t, and instead a transistor can be used to switch current directly from a voltage source:

In the circuit above, A is the IC output. It’s assumed that logical one is +5V, and the LED is a red one (with a 1.8 V drop and safe current of about 20 mA). If you switch LEDs or voltage levels, recalculate the value for the 180 Ω resistor using an LED calculator, and the 5.6 kΩ resistor using the “Choosing a suitable NPN transistor” section here.