How to get an internship in physics?

Talk to your high school physics teachers and see what they can do for you. Both of my AP physics teachers are capable of taking me up to my state university over the summer for physics research, and I fully intend to talk to them about it (it's a little early to bring it up now, and I don't think we're far enough in the class to have "wow'ed" them yet).

I have looked into interships relatively extensively, and most of the programs either require:
A.) for you to be a borderline genius with perfect SAT/ACT scores (NASA, MIT, programs offered by equally impressive organizations)
B.) foreign. (There are a surprising amount of internships that are only for under-represented ethnicities, or women, in an effort to get them the experience and attention that they duly deserve). or,
C.) Rich. There are many "internships" which aren't so much internships as they are paid-for research camps at universities. They would be, of course, a wonderful exposure to research, but are also costly and typically difficult to get into.

I've been lucky enough to have smart, easy-going physics teachers, who have the ablility to get me some exposure to college-level research (at least as far as I will be able to participate as a high school student). I would recommend that you express your interest in physics to your teachers, and ask them if they have any way of helping you get more exposure to the field.

If they don't, then, like you've mentioned, you can always email professors (something that I've never tried, nor know anything about) or you could apply to various internships around the country.

I've actually made a thread about this a little while ago, and here is one link that someone offered me: http://www.physics.isu.edu/internships/intenship.html

Another link someone gave me, although I didn't find this as helpful: http://see.orau.org/

A website that I found on my own that has many different programs: http://mitadmissions.org/blogs/entry/juniors_mit_and_other_summer_p

Hopefully this helps you out a bit. Good luck!