If a person is observed gripping their throat, this is recognized as the universal sign for choking. The colleague was likely eating a meal themselves and began to choke on a bolus larger than their esophagus could accommodate. As a witness and bystander, you should stand posterior to the patient and prepare to perform the Heimlich maneuver.
If the person is observed coughing, however, do not intervene and perform the technique quite yet. Their cough could remedy the situation and dislodge the item they are choking on of their own accord if forceful enough. If their coughing ceases, and they cannot laugh, talk, or cry, then it becomes time to provide first aid.
While behind the choking person, make a fist on your dominant hand with the knuckles of your thumb facing towards you. Then, firmly grasp this fist on its ulnar side with the other hand. Next, place your hands above the person's navel (belly button) or where you perceive their navel to be. Finally, forcefully thrust your hands into their abdomen five times as well as delivering five back blows with the palm of your hand to either shoulder blade before checking if the item has been dislodged or removed. To check, open the person's mouth and look into their throat. If you can see the item, do NOT reach in and try to dislodge it by hand; doing this can push the item back into the person's throat. Continue until the item removed or the person can continue to cough it up. If a cycle or two of abdominal thrusts, back blows, and checking are uneventful, call for help.
If the person loses consciousness, begin performing CPR, or cardiopulmonary resuscitation, and call for help.