Looking people straight in the eyes is important because it shows that you care and also shows self confidence. Begin with I'd like to introduce myself so that you have the other person's attention when you say your name. A firm handshake, once again, demonstrates your self confidence, but be sure you don't break the other person's arm or hand. Say your full name and immediately ask for theirs - then repeat their name while saying, Make sure you introduce with both first and last names. Telling someone where you work and your title is appropriate and may lead to many conversation topics these way introduce yourself.