How do you start a speech?  There are still human beings who wander this earth recommending beginning with a joke — and even attempting it themselves.  The problem with that is, for the majority of us who aren’t professional comedians, it’s hard to deliver jokes successfully.  As any professional will tell you, most jokes fall flat.  That’s why they have so many comebacks up their sleeves. 

It’s even harder to deliver a joke when you’re beginning a speech, because that’s when you’re most nervous.  So don’t try it.  Just don’t. 

Begin instead with something that will capture the audience’s attention in a way that’s relevant to what you’re talking about.  Frame the discussion in some way.  You might have a startling statistic.  You might have a factoid that puts things in perspective.  You might have a question to ask the audience that gets its attention.  You might have a personal anecdote — a relevant one, well told — that shows your interest in the subject matter.  "I first became aware of the plight of Asian yak herders when I was trekking up the North Face of Everest, looked down, and saw three yaks dangling off a cliff a thousand feet below me with three herders desperately trying to get them back on the thin ribbon of trail…." 

OK, so there probably aren’t yaks that high up on Everest, but you get the idea. 

Another great way to open is to involve the audience directly in some way.  Challenge them to do something, ask them questions about the topic, get their input in some fashion.  Try not to ask
"guess what’s in my head" questions, or difficult questions with right and wrong answers secretly designed to show off your expertise.  Instead, ask open-ended questions about the audience’s experience with the topic.  The point is to involve the audience and make them feel important and smart, not to make you feel important and smart. 

Finally, you can begin with a story.  Again, make it relevant to the topic.  Have it frame the discussion in some way that opens up new ideas for the audience rather than closes them down.  Have it make an emotional as well as intellectual point.  And tell it well.  Cut out the extraneous details.  Get clear on why the story is relevant and only include details that make the story comprehensible and refer to the frame. 

Fundamentally, your job is to include the audience and let them know, in the first 1-3 minutes, why they’re there, and why you’re there, why the topic is important, and what your theme and emotional attitude is toward that topic.  If you can do that you’re off and running.