For ourselves, we take the route of curious anthropologist. We try to stay open-minded and wait to decide whether we like something or not until we've given it a fair try. If we're feeling squeamish, we tell ourselves, "One bite won't kill me!" (We do draw the line if we're at all unsure about the food safety of the dish we're being served, though!)
For other people, we try to be patient. We offer bites of our food and tell them exactly what's in it. We have also found that describing how we first heard about this dish and what it is we like about it will set people at ease.
What about you? Are you an adventurous eater? Do you also try to convince your companions to try something new?