Situation: Person says hello to you.
Action: Say hello back.
Situation: Person doesn't say hello to you.
Action: Say hello to them.
Situation: Person initiates a conversation with you.
Action: Have a conversation. By which I don't mean answer all questions with 'yes', 'no' and 'don't know'. Volunteer enough information or an opinion to give them something to respond to.
Situation: You recognize that accent.
Action: Say, 'You sound local! Where are you from?'
If you are both in a home university, this is a big moment to share pride in your local area. After all, you are surrounded by people who have chosen to study in it. Discuss them.
If you are both on campus miles from home, then swap stories about how you got there. You've set off from the same point A and arrived at the same point B. Surely there's conversation in that!
Situation: You don't recognize that accent.
Action: Say, 'Oh! Where are you from?'
Situation: It's obvious where they're from. It says so on their t-shirt.
Action: Say, 'Oh! You're from *insert place-name*'
NB This is now a rich stem of conversation. Mine it. Discuss anything that you can think of which pertains to their homeland (without being offensive). Talk about sport; vacations; landmarks; use this opportunity to clear up urban myths and stereotypes. Make their home town/city/county/state the most interesting subject ever.
If that dries up, or you can't think of anything, default to their recent experiences. They've just had to pack up and move a certain distance. How was that for them then? Is it looking like a good decision so far?
Situation: Person is sitting in a corner on their own, people-watching and/or looking scared stiff.
Action: Assess the environment. If you can sit near, without invading personal space, do it. Wait a short time, so you're both used to being in proximity, then make a 'safe' comment. (Safe: general stuff about the goings-on in the room; weather; 'bit weird being here, isn't it?'). At the very least, say 'hello', though that might be a little too direct for this one.
A decent opening line is, 'Great spot for people watching, isn't it? I always feel a bit weird about just jumping in.'
Situation: Person is sitting alone crying or otherwise looking upset.
Action: Dude needs a friend. Go and be one. They are either a long way from home and homesick; figuring that they just made a terrible mistake being here; feeling like they will never fit in; or something very specific has occurred. Or all of the above. Or none of it. You'll never find out, if you don't go and do the decent thing.
A good opening line is, 'Hey, nothing is ever that bad really. What's up?' And, if you have a tissue handy, offer it.
In truth, it doesn't matter what you say, as long as you aren't laughing. This person just needs someone right there, right now.
Situation: Person is extremely loud and extrovert, taking the lead in a room full of strangers.
Action: Stand by them. Follow them. Stay as close as you can without being a creepy stalker. This is currently the top dog and you will find friendships through them. Hopefully even with them, as they have the skills in abundance that you lack.
Oh! And don't be fooled by them. They're just as intimidated. They just deal with it better; and the friendship that they are trying to attract is with you. Or, at least, people just like you. You fit the bill anyway, so answer the call to acquaintance.
Got a different scenario? Leave it in the comments and I'll add it to the list with my advice. Good luck!