Getting fired is gut wrenching and can cause panic over an uncertain future.  You need to treat the soon to be ex-employee with respect and professionalism.  Make your meeting fast, direct, and unwavering.  The best thing you can do for the person being fired is not fan any false hope by letting them beg for a job you do not want them to have.

Keep your conversation set on what is going to happen, not an explanation of how we got here.  Skip reviewing the employee's shortcomings, they only matter if you are going to work together to improve them.  Listing out deficiencies only serves to make the person getting terminated feel worse about themselves and opens the conversation up to an argument over the validity of the decision.

There are two events in the workplace that generate most lawsuits, hiring and firing.  You need to handle the termination meeting like your employee is there with an attorney.  This means being clear and concise about the termination, and any terms of separation.

Walk in prepared with company requirements like data privacy, non-compete with present clients, or company property to be returned in writing.  These should already be spelled out in your company handbook, but a separate document outlining separation helps alleviate the risk of missing key points and requirements.  If you are giving a severance, or the employee is entitled to access to a cobra these should be spelled out.  Anything that is left up in the air can later be fodder for a labor lawyer.

Always handle letting an employee go in person with a witness.  In a best case scenario the manager making the termination and a representative of the HR department will attend the meeting together.

This shows solidarity in the company, and gives you an added layer of protection against future claims of unfair treatment.  Additionally, having the extra person involved lessens the likelihood that there will be uncomfortable dead silences or that the conversation will stray away from the matter at hand.

Once you fire an employee it is time for them to leave.  You need to protect the company by ensuring the person doesn't log back in to their computer, take files, leave with company property, or talk with other employees.

Either you escort the employee, or have a person ready to handle supervising them leaving.  They are going to be upset and many will be looking for ways to lash out like deleting files or bad-mouthing you to fellow employees.  I doubt they will explain to their co-workers that you had solid reasons for letting them go.

Nothing brings down morale like negative gossip.  Once a person is fired there is a tendency for the management to want to consider the matter closed.  They made the hard decision, dismissed the employee, all solved.  This leaves the lingering problem of the staff filling in their own opinion as to why the employee is gone.

Have a short meeting and be simple and direct.  "(the employee) no longer works here."  Tell them your plan for the transition; plan to hire replacement, distribution of work, etc. "If you have any questions speak to (your HR)".  Do not discuss the separation (if they quit or were fired), or any of the reasoning behind it.  If a person asks why they are gone, tell them you respect every employees' privacy and the information between the company and the past employee stays in confidence.

Stop the rumor mill before it even starts.