Your handshake speaks. It must be firm. It should say: "I am intelligent. I am confident. And I am darn glad to meet you."
A weak, limp handshake says: "I'm not sure of myself. I am not sure about you. I am not sure why I got up this morning."If you are concerned that the person you are shaking hands with might be frail or suffering from arthritis and a firm handshake might hurt them, then mirror the pressure that person puts on your hand.
Your palm fits in the other person's palm. Seal the grasp by wrapping your fingers around the other person's hand. Don't squeeze the blood out of the other hand, but do give a good firm grip. No need to pump up and down like it's crack-the-whip. Just grasp.
Practice your handshake with friends and other professionals. If you mean business, if you want the job, if you want the sale, say it with a firm handshake.