It is important to understand that firing a person and letting a person go are diametrically opposite things. Whereas the latter could be result from work stoppages, the former is essentially based upon the performance of the individual. As such, this piece primarily talks about firing an employee.
Taking into account that fact that you have an adequate record of the employee's performance and you  have a grounded cause to fire him / her, you must chronologically follow these steps:

1. Firstly, you may need to seek your superior's permission or someone in Human Resources department to fire the person.
2. Adequately study the individual's present work assignments and the affect his / her firing will have on your department. Even if the person deemed to be fired is working on some critical project for the company, do not let the employee hold his job hostage even if the job they are performing is crucial to the company.
3. Always formulate an exit strategy. In order to least hamper the work of others, fix a stipulated time and date to terminate the employee. The most common day to fire employees is late Friday afternoons. Wish to know why? That is simply because it is the end of the work-week and other employees look forward more to going home than listening to someone being fired. When all return on Monday, the person fired will be a memory already.

While preparing for the employee's termination, take into account all necessary corporate paperwork  involved, what keys, locks, badges, computer passwords require necessary alterations, and back up the
employee's computer files. The employee, once fired must under no circumstance be allowed to touch his / her computer as allowing the same might lead to a threat of being sabotaged.

It is advisable to select a witness at the termination meeting as a neutral party regardless of the nature of the firing you expect. You must be prepared to record the termination if possible, as it would help you if the angry employee drags you to the court of law. If required, keep a box prepared for the employee in order to facilitate the process of emptying his / her desk.

Firing an employee is an important part of being a manager. You could also view it as a necessary occupational hazard. You must never procrastinate and also stop living in fear of firing someone for if you do, this fear will greatly retard your effectiveness as a manager. Also remember that if you are going to do it, you must do it right. Your employee must be aware of the fact that he / she was fired by a professional. The act of firing, if done properly, will win you your superiors' as well as your subordinates' respect, as well as the respect of the person you are firing.