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The interview handshake is one of the most important parts of the whole interview. If you are interviewing with an organization in the United States (and in many other countries), it is vital that you master how to shake the hand of the interviewer.
Let's first start with a disclaimer: Not all interviewers will shake your hand in the way that I'm about to describe. HOWEVER, in general, in the United States, it is a good idea to shake everyone's hand like this:
Also, avoid shaking lightly, with just the tips of the fingers. Here is why:
Shaking hands lightly indicates, in general, that you are not confident in yourself, that you are not trustworthy. As a result, interviewers may already have reservations about you, from the second you introduce yourself. They may subconsciously doubt your ability to do the job, to interact with customers, to present the organization well to the public.
Another note: If, in your country, men don't shake hands with women, or they just shake their hands lightly, not looking them in the eye, don't do that during a job interview where women are present, whether you're a man or a woman. Shake a woman's hand like you would shake a man's hand, not because she is a man or wants to be treated as one, but because it indicates respect for her position and professional abilities.
If you are a woman, shake a man's or woman's hand firmly. Grasp the whole hand, and greet each interviewer with confidence.
Finally, SMILE when you shake hands. A firm handshake, eye contact, and a smile can go a long way to creating a great first impression.
Remember: Whether you're a man or a woman, you were invited to the job interview for a reason. That reason is that the employer thinks you might be able to do the job well. During introductions and leave-taking at the end of the interview, shake each interviewer's hand firmly. Look each in the eye, smile, and introduce yourself. In the U.S., it shows you're ready to jump into the game (start working at the company) and that you are confident in your professional experience and skills to do the job well.