Ask for the letter early enough that the professor has plenty of time to write it. Provide him with your current transcript, your resume and a description of the position you are applying for or the school you are seeking admission to. The more information you provide the better the letter will come out. Make sure the professor will send his letter directly to someone's e-mail, or provide him with an addressed and stamped envelope.
Choose a professor whom you have impressed, either in class or in an extracurricular activity, or one who has mentored you in some way. He should be able to comment on your trials and successes as well as your overall demeanor.
Be genuinely polite when asking the professor. Ask if he feels he knows your work well enough to write a recommendation letter. This allows him a polite way out if, for whatever reason, he feels he cannot write the letter.
Give the professor a brief list of your relevant school work or activities that directly relate to him so that he will not have to struggle to recall specifics of your history.
Send the professor a "thank you" note right away and notify him of the outcome of your application later after you hear from the potential employer or the school.