In general, the less said to co-workers and other employees about an employee's termination, the better. People are naturally curious about what happened. However, you do not want to infringe on the terminated employee's privacy or leave yourself open to legal action because of something you have said.
If appropriate, you might want to review company policies and performance expectations with employees. This answers the any questions raised in employees' minds about can they can do to avoid being fired.
You should, however, be prepared to inform those impacted by the employee's departure, such as immediate co-workers, subordinates, and clients. Tell them that the employee no longer works for the company and how their duties and responsibilities will be carried out going forward.
Things to Consider
Preparing for a Termination
Outline of the Termination Process
Informing Other Employees