If you need a letter of recommendation from a faculty member, and we've worked closely together in some capacity beyond class (e.g., RA, TF, co-author, dissertation advisee, etc.), I'm happy to help out. However, if you have worked more closely with some other faculty member, a letter from that person is much more likely to be useful to you. Wherever you are applying will not merely want to know that someone endorses your candidacy (every letter does that!); the crucial component is that the person writing the letter knows you well, through a diverse array of experiences.
If you think that person is me, then please send me, along with your request, one email to firstname.lastname@example.org with the following as separate (nonzipped) attachments in PDF format (not Word and no paper please): copies of whatever documents you plan to submit to the organization to which you are applying that you think will be useful; a curriculum vitae; transcripts; test scores, etc.; and a confidential "sliced bread" memo (i.e., why I am better than...) addressed to me. This memo should not be a draft letter of recommendation, but instead should include a list of bullet points you want to make sure I remember when I start writing. These items can include how I got to know you and standard cv items (prizes won, etc.), but should also include relevant anecdotes that might make useful stories to illustrate characteristics of you or your work (e.g., solved a problem in five minutes that King had been working on full time for six weeks). This is not the time for modesty (only you and I will ever see it), and don't assume I will remember something if you exclude it. Include a very short (2-3 sentence) abstract or main finding of your thesis or other current work. If your record includes something negative (such as if you were in graduate school for too long), include your plausible explanation for what happened, if there is one.
I'll send all letters directly to the organization to which you're applying if you include an editable list of names and addresses, or to the Harvard dossier service, which sends them out for us. Please use email@example.com instead of my email if the organization to which you are applying uses a web interface that will send me emails.
As much lead time as you can provide would be appreciated.