Before you ask anyone to write a letter for you, explain why you think
that person would serve well in this capacity. Specifically, you
should be able to answer: What will this person add to your file that
might not be present otherwise? In what capacity has this person known
or worked with you, and how will that add to your file?
Once we have met to discuss who you should write for you, then you should ask them - well in advance of the deadline. When asking for a letter, put the question this way, "Do you think that you would be able to write a STRONG letter for me?"
The stronger your letters of recommendation, the better your chances of winning. To that end, provide your recommenders with copies of your personal statements, proposals, and resume.