If you Google “Au pair”, you’ll find many useful sites, such as http://www.aupair.com/, http://en.wikipedia.org/wiki/Au_pair, http://www.aupair-world.net/ – or even better, “Au pair US” http://www.aupairinamerica.com/, http://www.aupairusa.org/, http://www.usaupair.com/. I think this will answer all of your logistical questions, or at least definitely give you numbers/emails to contact for reliable info.
As far as personal experience and advice, I had au pairs (from France, in the US) when I was a child and it was wonderful, for me. I don’t know what it was like for them. They learned English, we learned French, my parents had a helper, and they had built-in work and housing. Likewise, my Hungarian friend (in her 20s) was an au pair in English speaking countries, and it was great experience for her, for language skills and also because she is an elementary school teacher and wants to run a childcare center some day. That’s post-university relevant work experience, and the bonus of getting to live in a foreign country. On the other hand, an American friend did it in Paris and it was a nightmare, and she had to move out after a couple months. So as above, it can be mixed.
But as @Marina said, it depends if it’s something you want to do, experience you specifically want (say, for future work with children), and if it’s worth deferring university (as she said, I personally wouldn’t). If you’re especially excited about spending time in the US, hoping work there might lead to other work, or might lead to getting into university in the US, I would think about it and research it carefully. Applying to US colleges/universities is done fairly far in advance (as in, you’d need to do everything really fast right NOW to apply for academic year 2010–11), and would be mostly based on your grades, test scores, recommendation letters, and any extra-curricular interests/activities – and I don’t know how much it would be helped by physically being in the US, or being an au pair. Residency could shift international/domestic status, which could affect scholarship eligibility, or give you in-state tuition (lower than out-of-state) for some public schools—but you’d really have to check on these things to see how it works with citizenship, etc. All in all without knowing any more about you or your situation I’d lean strongly toward going directly to university over the au pairing situation as you’ve presented it. I’m strongly in favor of living (and working, and traveling) abroad, and you can find ways to do that in summers, semesters off, and after college (I did all three of those!).