Approaching a stranger

Getting someone's attention

"Excuse me?" (Make sure to use a friendly tone of voice, with rising tone at the end) 

"Excuse me, sir?" or "Excuse me, ma'am?" 

Then: 

"Sorry to bother you, do you have a moment?" (Or, "do you have a minute?")

Asking for someone's name

if you've never seen them before:  

"I'm sorry, I don't believe we've met. I'm ____." (Extend a hand for a handshake if appropriate.)  "What's your name?"

 if you've seen them but haven't talked: 

"I've seen you around. I'm ______. What's your name?"

or, to observe a point of connection with them and ask for confirmation: 

 "You're in [so-and-so's class], right?"

"You live in [place], right? I've seen you around." 

if you've met them but forget their name:  

"I'm sorry, your name is escaping me." 

"Sorry, can you remind me, what's your name?"

 if you're asking their name after having talked for a while:

"What's your name, by the way? I don't believe we've met." 

"What's your name, by the way? I'm _____. 

Explaining what you want

If you're talking to a total stranger, do this soon. Get right to the point. People can get impatient quickly if they don't know why a stranger is talking to them.

 "I'm doing a project for _____. We're supposed to _______. I was wondering, would you mind answering a few questions?"

Elegantly taking leave

"Well, I'd better get going. Thanks for your help!" (or, "Good talking to you!")

"I'm off to [place]. How about you?" … "Want to head over together?"  (the subtext is, "do you want to keep talking?")