It really depends on the situation.
When approaching strangers in public (street, coffee shop, bar, etc), start with a simple hello, how are you? If they are receptive to small talk, ask them if you can show them something. If they say no, let them go about their business. If they say yes, show them one or two effects and move on to the next spectator/s or continue a conversation without performing. Remember the saying "Always leave them wanting more".
If you are in a social setting (party, event, etc.) bait people into asking you to see something. This is an idea from Eric Mead's The Tangled Web, and in my experience nearly always works. Engage in small talk with someone and ask someone what they do for a living. Inevitably they will ask what you do. Tell them you are a magician. Almost always they will ask to see something (this is ideal because then it seems more organic). If they don't, ask to show them something. Be respectful if they say no.
Approaching strangers is a great way to hone your chops, work on timing and misdirection, and build confidence. Narrow it down to a 2 or 3 effects and hit up as many strangers as possible. If you went to a busy place you could easily get a hundred plus 5-10 minute performances in a week.
When you start performing for strangers nerves will be a factor. Know the tricks well enough that the sleights are second nature.
I agree with Mr. Obrien, make your first trick as visual as possible. You'll have them hook line and sinker.
Flourishes are also a great way to draw attention to you.
Have a buddy film you as you go along. Go back and watch your performances. Cameras don't fall for misdirection. You'll quickly see the areas you need to work on. You'll be amazed at how quickly you'll progress, and the amount of confidence you can build by just getting out there and performing.