The process starts well before you ask for the letters.  Make sure that there are some professors who you know and who you keep in contact with.

Schools typically ask for three or four letters.

In considering who to ask for letters, keep in mind that it's important to have letters from faculty in who teach classes relevant to your field and so can speak to your ability to be successful in graduate school.  For example, if you are applying to a graduate program in economics at least two of your letters should be from economics professors as graduate programs in economics will take most seriously evaluations of your potential to complete graduate school that are made by people who completed graduate programs in your field.  If you have someone outside the economics department write you a letter, try to choose someone who can address skills that your other writers might not and who can address your ability in related fields.

Try to pick professors who can speak to your different strengths and abilities.  Maybe someone knows more about your writing skills, or you might have had more contact with someone outside of class, or worked with someone on a research project.

Don't hesitate to gently suggest what could be included in the letters.  For example, you might say "I think you could say more about my math skills than some of my other writers" or "I hope you might mention something about the paper I wrote." 

Provide your writers with some documentation such as your personal statement, courses you have taken, and other things that you might send to graduate schools.  Also provide whatever else you can to make their jobs easy including any forms they may need to complete.  If you stop by my office I will give you department letterheads and envelopes that you can address and stamp.