How should I ask for letters of recommendation?

If possible, schedule a meeting and ask in person. Talk to your professors about your interest in graduate school and where you should apply. Ask if they can write you a strong recommendation letter. 

If they agree to write you a letter, provide them with a list of the schools to which you are applying and the application deadlines, a copy of your transcripts, and a polished draft of your statement of purpose essay. You may want to write a personal note reminding the professor of your interactions and any particular accomplishments that they have direct knowledge of. Of course, if they request additional information such as a current resume or suggestions of strengths to highlight, you should provide that information as well.