The subject of how to write an e-mail to a professor or other senior scientist came up in our research group today. I'd like to add my two cents to some resources I found online here, here, and here (that you should spend five minutes to read). While the suggestions on these two websites are most relevant for students in a large enrollment general education course, many of the same pieces of advice should be followed when you want to contact a scientist at another university or lab. Basically, a professional e-mail should be treated more like a formal letter and not a text message to your BFF. And make sure you avoid common pitfalls (that will annoy the very person you're trying to impress).
1) First, can your question be answered by information available on their website (or on iLearn), elsewhere on the web, or by simply looking at their schedule posted outside their office door? Even senior students and grad students still ask me questions they can answer themselves. A good example from two weeks ago: A geology major graduating this semester who missed class to attend an optional geology field trip not related to any course he was taking asked "Did we miss the X lab while we were on the X field trip?". My response: "I don't know. Did you check iLearn?". I spend a lot of time maintaining course web sites to make things more convenient for both me and students. Use those resources.
2) Always (always) address the e-mail to "Dr. X" or "Prof. X". And don't forget to identify yourself: "My name is John Smith and I'm a graduate student working with Prof. Jane Doe at State University". Likewise, close your e-mail "Regards" or "Best Regards" and not "Thanks!" or nothing at all. Include a sensible subject line and keep the e-mail short, but provide enough information so that a response is easy. Don't write "May I have a copy of your 2008 paper?", write "May I have a copy of your Johnson et al. (2008) paper that appeared in the Journal of Important Scientific Discoveries"? Consider whether their response requires knowing more about the context of your question - what kinds of rocks are you working on? where did you collect your rocks? etc. It also can't hurt to start off with a compliment: "I very much enjoyed your recent paper in EPSL. May I ask a question about your EBSD results?".
3) It's always best to use your university e-mail account to send these kinds of e-mails. That makes it very clear you're actually a student at that university and not spam or some random wacko.
4) Get a professional e-mail address. "sillybear714@sfsu.edu" or "toadjuice@gmail.com" should be reserved for personal e-mail communication (if you must). Ideally, grab a firstname.lastname@univeristy.edu account, or (if it's too late for that) a firstname.lastname@gmail.com account.
5) Punctuate, capitalize appropriately, check your spelling, and write in complete sentences. A no-brainer really.
6) If you get a response to your e-mail, you need to take time to say "Thanks!". It's annoying to spend the time to answer questions, etc. and just have it disappear into the ether.
And if you're not sure how to write a tricky e-mail, run it past your advisor first... Particularly if there might be intellectual property issues with your e-mail or if there is any chance you might step on someone's research toes. Not sure? Ask your advisor.