Asking for a letter of recommendation

I have my eyes on doing a summer internship with a local biotech company. The application process requires three letters of recommendation from professors of classes I’ve taken. The problem is I’ve never talked or directly worked with any of them (lab classes were always instructed by grad students). The only way they would know me is by the grade they had given from their class.
What is the etiquette of asking for a letter?

This is a common situation for professors, so it won’t be considered a breach of etiquette. My suggestion is for you to draft the letters of recommendation yourself. Accompany the drafts with your resume, some work samples, maybe your transcript, your letter or essay of application to the internship, whatever you have that backs up what you put in the letter. The idea is to make it easy for them, while making it clear that what you’re saying is true. Obviously the professors will feel free to modify the letters but at least they won’t have to write something completely generic.

Thanks for the input Harriet.
I was just worried about the prof saying something like “You want me to write a letter. I don’t even know you. How can I recommend somebody I don’t know?”

You can also let the professor know who your TA was.

Take copies of your tests and any papers you wrote when you ask.

When I was a TA, I wrote several letters for undergrads in large seminar classes. As I had graded all of their work I was probably more qualified despite lacking an appropriate level of alphabet soup following my name.

In asking for a letter for myself, I always employed the following - “Would you feel comfortable writing me a good letter of recommendation?” It gives the potential writer the opportunity to decline and give the confidence that, if they accept, it will be a good letter. I never had anyone say no, but I did have one professor say that he had to read my final paper before letting me know whether he could write me a “good” letter of rec.