Here are some of my top tips, and a suggested template of a letter to contact a potential advisor at the end:
I came across your work through X (conference/paper/my professor X’s recommendation). I am very interested in your approach to (topic) using (method/specific thing they do that interests you).
I’m writing to inquire if you are accepting PhD students in your lab for fall 2016?
I am aiming to pursue a PhD dissertation focusing on X topic, specifically looking at the question of X puzzle in X case for X purpose.
My background is in X bachelors from X university/Y masters from Y university. My research to date has focused on X, which I investigated most recently in my master’s thesis on X topic in X place, finding that X key highlight (please see attached thesis FYI). I have written about this work in a popular science blog here (link) and am currently preparing the manuscript for submission to the journal of X with my supervisor X.
I also have experience in X business/NGO/policy/government, where I accomplished X. For more details, please see my attached CV.
Regarding funding, I am currently applying for funding from X, X and X scholarship agencies to support the project I’ve outlined above. If there are any additional funding sources that you think might be a good fit to support this work, I would really appreciate any tips. And of course, if you have any currently funded projects that could support a PhD student, I would love to hear about them.
Thank you very much for your time and I look forward to hearing from you.
If you don’t hear back from them in 2 weeks, resend your message with a polite note at the top: “Dear Dr. X, I thought my earlier message may have caught you at a busy time. I’m still very keen to pursue a PhD in your lab, and hoping you can let me know if you are accepting new students next fall. Thank you, X”
If there’s someone you’re really excited about who hasn’t gotten back to you, consider picking up the phone to call them. Bold move, but it just might work! People get a bajillion emails, but few phone calls nowadays. Practice a shortened version of the text above to ask them.
It’s smart to apply to at least several schools (I just checked and I applied to seven PhD programs, which now seems excessive- but at least three is good). You don’t know where you’ll get in, and you’ll have to consider personal factors about where you want to live, so it’s good to have options.
Most advisors will be contacted by many students and will have many applicants for each open position in their lab. So, you both are on the lookout for the person who will be the best fit! Most advisors will understand this (some may even ask where else you are applying).
That said, if you apply for external fellowships, you may have to specify your top choice for where you want to go and who you want to work with (depending on the fellowship). In this case, it’s important to share your plans with your potential advisor and get their agreement to support your application. In any case, if you really click with a potential advisor, consider asking them to give you feedback on your external fellowship application (for something like NSF GRFP, not for their own university applications where they would have a conflict of interest). Hopefully their comments can help you strengthen your proposal.
In any case, good communication with a potential advisor is important, so ask them questions to clarify expectations or any points of confusion.
Hope this helps- let me know if you have any comments!