This page gives some advice for people who are considering asking me for a recommendation letter. It is inspired by my former professor Ravi Vakil's excellent page on the same topic, but tailored to my earlier career stage.
This depends on a few things: how well I know you, how well you did in my class(es), and what you're applying for. For example, if you're applying for something relatively low-stakes (e.g. summer schools, some departmental programs), I might only be asked to attest that you're a serious student who is likely to benefit from the program. I can often make this judgment based on knowing you for less than a full semester. However, if you're applying for something more competitive (REU, undergraduate or transfer admissions, graduate school), I am unlikely to be able to write you a useful letter unless (1) I have taught you for at least a full semester, and (2) you earned some flavor of A in my class.
Even if I can write you a strong letter, it may in some situations be worth considering asking someone else for seniority reasons. (As a postdoc, I am still relatively low on the academic totem pole.) If Famous Professor X can write a letter saying that you're in the top 5% of all students they've had in the last 20 years, that will carry much more weight than me saying that you were in the top 5% of my students last year. On the flip side, you definitely shouldn't ask someone for a letter just because they're famous—a strong and detailed letter beats a lukewarm letter no matter who it's from.
If you're not sure whether I'm the right person, then feel free to ask—I'd be happy to talk through your options with you. Needless to say, it is in your best interest to have this conversation sooner rather than later.
The following information is useful for me to consult when writing my letter. Please send it to me as early as you can (a month's notice is ideal, although it's okay if some things come later):
Finally, if your application ends up being successful, I'd appreciate hearing where you got in. It's nice knowing what became of my old students, and it may help provide a point of comparison for my future rec letters (e.g. "Future Student Y reminds me of a student I once had who got into Prestigious School Z...").