Make note of something pleasant

"This dip is delicious!" "Nice turnout for this event!"

There's something positive to say in nearly every situation, so find it and say it. Don't say something negative because it's much too risky.

The one exception to the no-negatives rule is the weather. 

If you're in the midst of a heat wave, cold snap, or torrential downpour, remarking on the unusual weather is often a good way to start a conversation.

"Excuse me, do you know what time the next session starts?" 

Even if you already know the answer, asking for information can be a great way to start someone talking with you, because everyone likes to feel helpful.

"Could you reach that item on the top shelf for me?" 

Requests for assistance are another way to make someone feel helpful. Just make sure whatever you ask for is something the listener can provide without much inconvenience.

"Can I help you carry that large box?" 

The listener will be inclined to like you and trust you because you've helped out. Be careful not to be intrusive or excessive.

"What did you think of that speech?" "Did you get a lot out of this workshop?" 

Most people like knowing that others are interested in their opinions and will be happy to respond.

Naming someone you both know will tell the listener you are part of his or her extended social circle. 

Many people will begin thinking of you as someone they know or should know. Be careful, though, that their relationship with your shared acquaintance is on good terms.

Does the listener come from the same town or region like you? Did you attend the same high school or college? 

Any common ground is a good way to start someone talking, especially if you use it as a reason to ask for information or advice.

This works when you're wondering what to say to someone prominent. You'll never insult someone by saying, "I really love your work," or "I thought your last blog post was very insightful."

Three caveats: Don't fawn, don't make the mistake of critiquing the listener and only offer praise if you genuinely mean it.

"That scarf is a great color on you." Most people like it when others appreciate their taste, so they will likely want to engage with you.

Don't comment on the listener's own physical appearance - it has the potential to be creepy.

Walk up to the person, stick out your hand and say, "Hi, I'm so-and-so. I just wanted to introduce myself." 

The fact that you went out of your way to meet will make the listener feel important. It will probably make the person want to talk to you, as well.