What is the right approach for sending emails to contact the graduate students in the graduate schools that we are applying to?
Some questions to ask current graduate students are suggested in this related question.
When asking such questions by email, what are things to consider to maximize the chances of a useful response?
My email has been posted at both my MSc and PhD department's website. I do not mind cold emails, even before applications are submitted. I answer this question maybe 3-4 times a year before applications are even due: "If you could go back in time and start over, would you still come back?". Applications cost money, I don't mind spending an hour or two every year helping people whose shoes I was once in.
Most people are the same I'd think.
Edit:
I'll read anything with my advisor's name in the email, so, if you title the email "Prospective student for Advisor" or something like that, then It will probably at least get read.
Once you have been admitted, the department will typically help put you in contact with graduate students. Of course they will select the most enthusiastic ones, so it can be helpful to reach out to others to get a better sample (for example, students in your research area or who are working with potential advisors). You can generally find contact information for graduate students on the departmental web page or on their personal web pages, and it's reasonable to send a quick e-mail. You can ask whatever you'd like, but you should remember that it's not really their job to tell you about the department. It's best not to ask questions you can get answers to elsewhere (for example, don't ask about degree requirements), awkward questions (such as departmental gossip they might be uncomfortable discussing, especially in writing), or repeated/demanding questions (after all, they are doing you a favor).
On the other hand, I don't think you should contact graduate students before being admitted. Most graduate schools receive substantially more applications than they will be able to accept, and sometimes far more. It's not efficient to spend a lot of time telling people about the department if they are probably not going to be admitted anyway. Instead, that can wait until the admissions decisions have been made. (Plus you'll generally get more enthusiastic responses once you've been admitted.)
When I was applying to grad schools, I cold e-mailed some people and got some very helpful responses.
In the first place, you might start by apologizing for cold e-mailing them. If there are any extenuating circumstances, you might explain them. I e-mailed under two different circumstances:
I was accepted by program X, and got the sense that I didn't want to go X, and wasn't planning to fly cross-country to visit -- but I wanted to hear from a couple of people at X first.
I was waitlisted by program Y and I was pretty sure I wanted to go there. But things were going down to the wire, and I didn't get the opportunity to visit before the acceptance deadline.
You will optimize your chances by writing your e-mail in a way that expresses your gratitude and a little bit of your personality. Ask them questions that you can't easily learn for yourself by browsing the department's website. And write your e-mail in a way that makes it clear that you are hoping for a response but then won't need anything else from them. (Unless you end up visiting later, in which case I recommend offering to buy them lunch or a beer.)
