Here is that sort of email:
“Dear Professor Kelsky, I am a student at XXX College and I’m thinking about graduate school/doing research on xxx and I’m getting in touch to ask if you can give me any advice or direction about that. Sincerely, student X”
This is an instant-delete email.
Here is what an email to a professor should look like:
“Dear Professor XXX,
I am a student at XXX College with a major in xxx. I am a junior and will be graduating next May. I have a 4.0 GPA and experience in our college’s summer program in xxx.
I am planning to attend graduate school in xxx, with a focus on xxx. In one of my classes, “xxx,” which was taught by Professor XXX, I had the chance to read your article, “xxxx.” I really enjoyed it, and it gave me many ideas for my future research. I have been exploring graduate programs where I can work on this topic.
I hope you don’t mind my getting in touch, but I’d like to inquire whether you are currently accepting graduate students. And if you are, if you’d be willing to talk to me a bit more, by email or on the phone, or in person if I can arrange a campus visit, about my graduate school plans. I have explored your department’s graduate school website in detail, and it seems like an excellent fit for me because of its emphasis on xx and xx, but I still have a few specific questions about xx and xxx that I’d like to talk to you about.
I know you’re very busy so I appreciate any time you can give me. Thanks very much,