How do you ask for letters of recommendation?
Ask junior year teachers in core academic subjects who know you as a person, not simply the ones who gave the highest grades. Ask in person, in the spring if you can, give them a month, and hand them something to work from. A teacher who saw you struggle and improve writes a better letter than one who barely noticed you.
Who to ask
Most colleges want one or two teachers from junior year in core academic subjects, plus the school counselor. Choose for knowledge of you rather than for the grade. A B in a class where the teacher watched you work through something produces a specific letter. An A in a lecture hall where you never spoke produces a generic one, and generic letters are close to worthless.
When and how
Spring of junior year if possible, before every classmate asks the same three teachers in September. Ask in person, and ask whether they feel they can write a strong letter. That word gives a teacher a graceful way to decline, which is a favor to you.
What to give them
A short document: the classes you took with them, a couple of specific moments you remember from that class, what you are applying to study, and the deadlines. You are not telling them what to write. You are reminding a person with a hundred and fifty students of the details only you remember.
The parts students forget
Waive your right to read the letters; letters that have not been waived are discounted. Follow the school's process for submissions. And write a thank you afterward, and tell them where you ended up. They wrote it because they cared how it turned out.