I can respond most effectively if you provide me 2 or more weeks notice prior to my having to submit the letter. Less than this notice you risk that I may not be able to submit the letter on time. When you request a letter from me, please provide me detailed information about what you are applying for, along with as much of your application information as possible (for example, a draft of application essays or cover letters, a CV or resume).
If you want me to write a strong letter for you, please read Leonard Cassuto's wise advice - all of which applies to me as well as to him. It also applies to multiple requests - if you sent me all of this information when you requested a letter a couple of months ago, send it again this time too. This will help me personalize your letter, which will make it more effective.
In general, I do not provide letters to students to submit with their applications. In nearly all cases that I am aware of, employers, graduate schools, and fellowships provide faculty instructions for how to submit their letters directly to the reviewers. Please provide me with this information.
Finally, if you only know me from taking one of my larger lecture classes, please keep in mind that I probably do not know you very well, and you are almost certainly better off asking for a letter from a professor who knows you better, and will thus write a more detailed and personalized letter. While I will write letters for students who obtain A grades in large classes, the letters are brief and formulaic unless you have made yourself known to me outside of the context of a large class. This kind of letter is not very effective support. In general I will only write letters for students who obtained an A in these large classes.