Approaching strangers can be difficult but, like anything else, it can be mastered with a little practice. here's my tips:
1) Start with couples. They are easier to approach and there's a level of safety when your dealing with a group. After a pic or two together, separate them into individuals if there's a level of comfort.
2) Be extremely polite like you were approaching a head of state or famous actor
3) Always briefly explain what the shot is for and where it will be used... and offer free copies.
4) Hand them a business card ($10 worth of business cards can get you introductions, back-stage passes, media access, and a "get out of jail free" card. Seriously. Best $10 you'll spend in photography!!)
5) A little flattery will go a long way. A lot will end in a restraining order.
6) Be prepared for a wide variety of reactions. Most of the time you'll get a few snaps, a few times you'll be treated like a panhandler, but sometimes the person will be very into it. Go with the flow. Be chatty. Ask them if they mind if you take a few more shots. Let them set the pace.
7) Confidence. Boldly walk up and introduce yourself like you've done this a million times. People will read your body language long before they hear your words.
8) Thank them at the end. Make sure you explain where they can see your shots, how long it will take for the shot to be posted, and how they can get a hold of you (business cards!!!)
9) Immediately find someone else to work with.
10) Dress the part. Prepare as if you were going on a job interview. Nicer cloths, good hygiene, positive attitude. Besides the business cards I also have a few nice polo's with our "iris" logo and web address printed on them. Gives the appearance that you're truly a pro artist not just some dude with a camera. It will also help you psychologically when you're wearing your "business casual" uniform with matching business cards (Yes, I mentioned business cards 4 times... they are THAT useful!) and that confidence will be easily read by your potential subject.