First, work on your shyness. Get better at talking to strangers at home. Look for books and tapes (and even web sites) written for salesmen, street photographers, and so on for tricks-of-the-trade.
A photography trick I haven't tried yet: asking people if they would like you to take their picture supposedly works better than asking them if you can take their picture. And offer to send them prints if they contact you (have cards ready).
If you're travelling to the US, be aware that in major metropolitan areas, if you look foreign or speak with an accent, but don't look like a tourist, most people will assume you're just another immigrant who's lived here for years and thus (most of the time) politely refrain from bothering you with questions about where you're from and so on.
If you go to the parts of rural America where say, the population of the apartment complex I live in here in California would have a significant impact on the "diversity" of a lot of towns of 50,000 people, lots of people will be curious about you.
The most dead simple trick for conversations is, if you see something you're curious about, stop someone and ask them about it. Or ask for directions even if you're pretty sure how to get where you want to go. Even if there's something weird and fascinating on TV in your hotel, go down to the hotel bar if there's a TV there and ask about it!
Ask about things you're sincerely interested in (better yet, things you know something about). Food, local history, architecture, the arts, even religion. Be lavish in your praise for what you like or admire. "Do you know when that building was built? It's very beautiful.", that kind of thing.
I gotta get my two cents in, for people from the US:
Pretending you're Canadian while traveling is just disgusting. I can't believe people actually talk about doing this. Just don't. Do you regularly lie when making new friends? Most people won't be rude to you. Don't be afraid of the "foreign peril", don't be a stereotype, speak from the heart, and put YOUR guard down. Again, this is a shyness thing that you might want to work on before leaving home: a lot of people tend to put up a front of a sort of stereotype of their social class when talking to strangers. That kind of shallow mask will come across as rude when you're in a foreign country. And yes, wherever you're from, it might take a few times out of your fishbowl before you even realize what I'm talking about here. That's OK: better late than never.
And you don't have to apologize for America, or even for whatever US policy (or president) is in the papers that year. Only an asshole would expect you to. Do listen, though. Most people, the world over, are no more politically sophisticated than "Joe Sixpack" but they're getting different stuff from their local media. Hearing out a political crank overseas is a worthwhile experience especially if you buy too heavily into all this nonsense about how misinformed American political discourse is!
Oh, all that said: if you speak a European language other than english, and other than that of the country you're visiting, well enough to hold a real conversation, in Europe asking someone if they speak ______ or English will often win you some points. Even if those countries have some historical differences. Yes, that sometimes plays on people's assumptions, but that's interesting in itself to see.
If you're open and outgoing, you'll find people who'll embarrass you with their hospitality---old-fashioned hospitality involves manners and traditions that are dying out in the US---almost anywhere. Be ready to reciprocate when you can! This takes work and discipline too!
Leave your finicky eating at home. Eat everything. For the love of god, if you're invited to someone's home, eat everything. Practice at home: even in small towns there's lots of opportunities to try new foods if you seek them out. Middle-class Americans often have a horrible habit of bossing waiting staff around boorishly, also. Learn not to do it at home (it's rude here too) and you'll be better off when traveling.
And by the way: yes, learning as much of you can of the language helps. No, learning a hundred words or so of tourist vocabulary is not a major intellectual challenge or accomplishment. Just do it. Get some tapes or something. The fact that this is impractical for whirlwind tours of 12 foreign countries is a good argument against taking whirlwind tours. Be as outrageously polite as you possibly can be, always. Learn to say something closer to "Pardon me, but I don't understand very much ________. Do you speak any English?" than to "Hey, do you speak English?" And if your pronunciation is rotten, speak slowly and with a little bit of exaggerated effort, and people will realize it's not easy for you but you're trying. Letting people see the difficulty you're having will put them at ease and give them the confidence to try to talk to you if they had a hard time with English in school, too.