At the time I had 8 classes. 6 of them were required: math, english, history, etc., and 2 were free electives: sports, music, technical (computers and woodshop). As a 11yo these were the few freedoms we were allowed in school and the work didn't feel like work. I enjoyed making music. I enjoyed making stupid, wooden gifts for my family and friends. So the counsellor says we're dropping your 2 electives so you can have take our gifted classes. And that is when I hoped right out of it.
Now that is the gifted (also called ESL) program in none exceptional schools. It's usually just an extra class. There are schools of excellence, governor's school, magnet school, etc. Which focus on different curriculum. These will have an emphasis around math, language, arts, sports. You apply by filing an application or submitting a portfolio. Some, you have to be nominated by your teachers.
When I was growing up anyone who was nominated by their teachers would simply skip grades or get shifted into an honours program if it was available for their level.
Just as I was graduating high school however, all the gifted programs were phased out as being unnecessary (or unfair depending on whom you talked to). There was much hay made about the tight school budget needing to go to support students who were being left behind by the new national testing standards.
Now, though, ten years later, they have magnet schools for the talented which are by nomination only.
That was back in the 1980s and 1990s; not sure how things have changed.
I have to say... I thought our school system did a good job with gifted students. We had some classes with other gifted kids and a lot of classes with the school's general population. We weren't treated as elite freaks or anything, were never told we were "better", and all in all I think they did it right.