1. Make eye contact. This is a great way to connect to someone. They know you are interested. Eye contact is used in almost everything: getting a waiter/waitress to come to your table, telling somebody to come over, or showing people you understand. If you want to get to know somebody better, eye contact will always be the first step.
2.Smile. The law of reciprocity says to give what you want. You will be amazed how many people smile back if you smile at them. Be sure it is a relaxed smile. There really isn't a right or wrong way to smile, so relax.
3. Say "Hello" or some other greeting. Be a little creative if you like, especially if you can determine with certainty his/her first language. Try to greet with that language. "Aloha" and "Guten Tag" are two favorites. Be careful not to make assumptions about an individual's language based solely upon his/her appearance, however, as he/she could be offended if you guess incorrectly. Be warned that the more creative you are, the more likely they are to not understand you.
4. Evaluate the situation. If they are not maintaining eye contact with you, did not smile back, or did not respond to your greeting, then they may be otherwise distracted or this may not be a good time. If you will have an opportunity to talk to them soon (i.e. you see them on a regular basis) then you may want to wait. Otherwise continue.
5. Maintain eye contact and keep smiling, but be relaxed. Maintaining eye contact shows you are interested and intent, and generally everyone likes a smile.
6. Comment about something mutual: the weather, sports, work (if you work together), your location or situation (stuck in an elevator), traffic, etc. Talk about something you can both relate to, but not too personal. It's a great way to break the ice.
7. Tell them your name. Again, on the law of reciprocity, if you offer your first and last name then they will typically tell you theirs. But, it's better to start with your first name.
8. Offer your hand. If you offer your hand, then they will usually shake it.
9. Ask them a question, especially about Family, Occupation or Recreation (remember what questions are FOR - see warnings). These are great things to ask questions about if you cannot think of anything else. It is important when asking questions that you are not interrogating them. Most people love to talk about themselves, but if they don't, then don't press them.
10. Listen to what they say. Remember details. Ask more questions that show you were paying attention.
11. Get a question in return. Eventually they will probably ask you a question, too (law of reciprocity). This is called a conversation. Answer their questions, but don't get too caught up talking about yourself.