If its a digital IC, then the output will have two states, High (Vcc) or Low (0V). So if you connect a load between the output and Vcc, the IC will have to SINK the current. If you connect the load between the output and the 0V line, the IC will have to SOURCE the current. You look up the sink and source currents from the data sheet for your IC.
Example TTL chip Isink = 10 mA driving a LED from the Vcc ( 5V). So LED drops about 2 V, so the series resistor must drop 5-2 = 3 V at 10 mA so R = 3/.01 = 300 ohms. Because the output of a TTL chip is not a perfect switch, its output will not be a true 0V, but .4V? , so the 3V, in reality will be 2.6V so you could safely go to 270 ohms. Lower then that and you will have to measure the current and select the resistor to suit..
Frank