Faculty are happy to write letters of recommendation. It is of course better for you to have more than just passing or casual experience with a recommender. How much and what kind of shared experience of course can't be determined by any fixed rules. But writers of recommendation letters feel that they should indicate how well qualified they are to comment on a student or former student. Readers will know how to factor in the quality of the information and assessment being made by the writer. Keep in mind that letter writers know that letter readers prefer eyewitness accounts to hearsay.
A strong letter of recommendation might well make reference to special experiences that epitomize your good character, breadth or depth of experiences or fine intellectual skills. So in considering someone to be a recommender, you might consder someone with whom your fund of experiences is reasonably rich; that may mean that they are also better aware of flaws or blemishes, but you have to trust that your recomender will be judicious. Such trust is very rarely misplaced.
Give the professor an opportunity to tell you how strong a letter she or he can honestly write for you. If this particular person cannot write a strong letter, think about thanking him or her for their candor and asking someone else to write.
Provide an application form if there is one. Some application forms envision you filling out the basic information about the recommender; the recommender then needs only to fill out the form and sign. Having preparatory work done is appreciated.
Make sure the due date is clear to your recommender; it might be good to provide it in writing.
It might help for you to list the course(s) you have had with this professor; you might also indicate work you did for a course; providing copies of work done to a recommender might be wise.
At Carlton College they ask for the following information, to go into a file for future reference in writing recommendation letters.
1. Name; 2. Permanent address (where you can always be reached) and phone number; 3. Age; 4. Class; 5. Major; 6. "Minors" (or other departments in which you have done extensive work); 7. Mathematical background (including math, computer, statistics, methodology) or other special skills; 8. Summer experiences; 9. Work experience at college; 10. How good in general has your academic record been? In what courses did you excel? Why? In what courses were you weak? Why?; 11. What about extra-curricular activities? Have you been active or merely a member?; 12. What kind of job would you like to be recommended for? Is there any other information you think would be helpful to us in preparing these letters? What aspects of your background, abilities, and experience do you feel justify recommending you for this position? Are there any other specific strengths or weaknesses you would like us to extol or explain in our recommendations?
If called for in the application process, you will provide the envelope and postage. Otherwise it is probably more appropriate for the recommender to use department stationary; the department can pay the postage.
It is an important courtesy, too often overlooked, for the student or former student to let recommenders know what the outcome was of the application (they made the effort to write the letter; accordingly, they deserve some feedback). And of course there is no shame in an unsuccessful application.
Recommendation writers keep copies. They know how to rewrite an older letter either to take account of new information that has become available since a letter was previously written, or to redo a letter in light of differences in what kinds of assessments and information a new reader will want.