Instead of embarrassing the employee in front of his/her colleagues, it is recommended that you take him/her to a private room and also ask another manager to accompany you in order to take notes. However, the manager should not be involved in the actual disciplining process.
Instead of making it personal, focus on the actual offense, as opposed to the employee. As a manager or the boss, you need to be very clear with the employee; make sure you let him/her know what the offense was, and exactly how it goes against the policies of the company.
You need to explain how the behaviour of the employee has had or can have negative effects on the company. If the offense of the employee has had a direct impact on other employees then you need to reveal this fact to the troublemaker - let him/her know that because of her/him, the company and its employees are suffering a great deal.
Do not keep speaking without pausing or allowing the employee to respond. It is always better to speak your mind, and then let the employee reply, if he/she wishes to say anything in his/her defense, or clear his/her name. Do not interrupt when the employee is speaking - respond appropriately only when he/she is done talking. You need to make sure that your response is solid enough to leave the employee satisfied, even if it is not what he/she was hoping to hear.
End the meeting conclusively, by giving the employee a defined plan of action, and making your expectations from him/her very clear.
You need to give a clear warning to the employee, and let him/her know that punitive action will be taken according to company policy if the offense is repeated. The employee needs to know exactly what will happen next time; i.e. whether he/she will get a written warning or be terminated.
It is also helpful to ask the employee how you can support him/her in bringing about a positive change in his/her work ethics. The objective should be to make the employee feel valued.