How to meet people and make friends while on a vacation?
Meeting people is something that comes easily to some, and not at all to others. The key to meeting people on the road is to make use of any resources you have at hand, but to not be dependent on them. One strategy that you can use to meet people when traveling is to become a regular at a few different places near where you're staying. Try out a few restaurants and coffee shops and bookstores and choose one of each to frequent. Get to know the employees and the owners, and eventually you'll also start to meet the other frequent customers. Seeing someone repeatedly is a big step toward recognizing them as someone like you, rather than an outsider, and removing the 'outsider stigma' is a big part of what we're trying to do here.
A few broad tips that will help you make new friends, regardless of the situation, context or strategies you use:
It seems obvious, but most people — especially when nervous — will unconsciously become defensive and will reflexively grimace or frown or have upset-eyes as a response. Worse, many people will become clipped, abrupt or otherwise rude, going into protect myself mode and trying to fight off the threat. Keep this at the forefront of your mind: be friendly. Be someone that other people want to be around.
This is a great way to start a conversation, and to simply show your good intentions to a stranger without even having to know their name. Pick up something they dropped, help them carry their groceries, or otherwise make their lives a little easier. Relationships are based on having an equal exchange of value (healthy ones, anyway), so by providing value from the beginning, you're subtly indicating that you would be a good person to have around, and the other person will be more likely to want to give value back (perhaps by introducing themselves).
One thing that makes the 'stranger danger' alarm go off in peoples' heads is not knowing who you are, what you want and why you are around them. Our animal instincts pump out all the worst chemicals when we are unsure of what's going on around us, so you want to make yourself as easily identifiable and comprehensible by that lizard brain as possible. Make sure your clothing, posture, facial expression and actions all reflect who you are and what you're up to.
Don't be weird
If the person you're approaching seems to be pretty weird, this rule may not apply, but in general, avoid trying to be impressively off-center. Instead of making you seem endearing (as you probably want it to), your weirdness will make you seem like an unknown quantity, or worse, a known quantity that their brain perceives as a threat.
Finally, meeting people is for naught if they have no way to get in touch with you. Before you start trying to build local connections in earnest, have a mobile phone number you can hand out and be ready to connect online as well. Facebook seems to be the common way to stay in touch as it allows strangers to become less strange and more familiar with each other, and with little commitment, though emails are pretty good, too.