What category of controlled substance was it?
I received a caution for possessing controlled drug - Class A - Other in October 2007.
I attended the US Embassy in August 2009 with the intention of gaining a B-2 Tourism / Holiday visa.
The interview was very short winded. The interviewer was a female Yank. She asked me about the caution, whether I was still using any drugs etc.
Put it all down to mispent youth, misuse on a night out etc.
She approved the Visa with a 10 year expiry there and then. You are obliged to re-apply every 10 years for your Visa's by the way.
There wasn't much else to it to be honest. I went in a suit but I think I was very much in the minority.
The embassy is remarkably busy so expect to spend the full day there and way past your appointment schedule time.
Take a magazine / book with because you aren't allowed any electronics, phone etc.
Just be polite, confident and re-assuring that it was a one off and it has made you re-assess your priorities and drug "misuse" is behind you.