1) First, is it necessary to email your professor? Would a face-to-face meeting be better? Is it best left unsaid? Professors are inundated with messages from students that are either unnecessary or would be better said in person. If email is the best option, proceed to #2.
2) [salutation (optional)] [comma] [space] [honorific] [comma or dash] [new paragraph]. For instance:
(Hi), Dr. Frankenstein–
I hear you’re working on a new monster, and I’d love to be considered for your lab assistant position. . .
3) No need to introduce yourself by name in the first sentence; gmail tells your professor who’s writing before she opens the email. Instead, get to the point, assuming your professor is so busy she hardly has time to open your email, let alone read it. Often, this is true.
4) If you have an ask, ask as soon as possible in the email. In journalism this is called the “lead”, or the most important point, and it’s a cardinal sin to “bury the lead”.
5) No large blocks of text. Two lines is a paragraph’s limit; three is pushing it; four is a sign of immaturity; five or more indicates a psychotic breakdown.
6) Make it easy for the professor to respond. Suggest times to meet, rather than ask her to.
7) Only use exclamation points when you’re screaming in delight, which is probably never.