In an earlier post I explained the reasons that you must never ask your TA for letters of recommendation. All of your letters must come from faculty, preferably full-time faculty in your major department or one closely affiliated.
Now I’ll discuss some tips for accomplishing this.
If you don’t know the professor well, then get to know her. Go to her office hours. Discuss your graduate school aspirations with her. Ask her for guidance. Remind her gently who you are and what grade you are getting/got. Bring in a paper that you wrote for her course.
And make sure, when choosing your courses for next term, that you enroll in courses that are taught by faculty members and not by TAs. It is OK to call the department to ask. You may also simply search the name of the instructor on your university website people/department directory to see if they turn up listed as faculty or as student.
As you get into upper division classes, make it a central goal to work with professors. If you have dreams of graduate school, you must gather around you at least two and preferably three faculty members, ie, actual professors employed by your institution, who will write you strong letters of recommendation.
And, what you are seeking are professor who are full-time faculty members of the school. While “visiting”/”adjunct” professors will do in a pinch, they are not as good (for the same reasons listed above) as regular, permanent, full-time faculty from your college or university, and preferably from your major.
You want the professor to enthusiastically agree to write the letter. Any hesitation or reluctance….move on to someone else.
And, do NOT expect to see the letter, or to in any way tell the professor what to write. This is a trust exercise. And, professors know the stakes.
In sum: do not be intimidated! It is part of a professor’s job to meet with undergraduates AND to write them letters. YOU ARE ENTITLED to ask faculty members to write recommendations. And as long as the professor is genuinely supportive of you, the professor has an obligation to fulfill this professional responsibility.