While it’s unlikely that a good handshake will land you your next position on its own, it will strengthen the first impression you make with a potential employer.
In a business setting, the person in a higher position of authority should initiate the handshake. Look them directly in the eye, and give a verbal greeting as well.
You should grip the other persons hand firmly with your right hand, but without crushing their hand. Your thumb should point up towards the sky, unless your interviewer moves your hand in a different way. A good handshake lasts somewhere between two and five seconds, and generally is two pumps (up down, up down).
If you’re not yet comfortable with strong professional handshakes, ask a friend to practice with you and give you a critique so you know how to improve.