How can I cure myself of mild anxiety - without using medication?

Only within the last 3 years or so have I experienced symptoms of mild anxiety off and on. I can't really pinpoint what causes these little panic attacks - but oftentimes I feel like I am going to vomit, especially if I am out to dinner, whether on a date OR with a big group of people, even if they are people I feel comfortable with! And I almost always do, or else I can't eat more than 2 bites. Another symptom is that I shake and feel cold without meaning to. What can I do to combat this??