It was a short e-mail (two paragraphs) just telling them I was applying (or had applied, I only wrote in December or so) to this program and their work in particular had caught my attention. (naming particular things, such as, books/articles you read and they wrote, classes they are teaching and you are particularly interested in.) You then also want to include how this links to your interest and to your proposed dissertation project as you have mentioned or will mention it in your
statement of purpose. It can also be a genuine question to confirm or ask whether your proposed project would be something they would be interested in supervising and whether it falls within their field of expertise. (All of this depends on the particular situation) So you add your fields of interest while discussing this. All of this should be as brief as possible of course, I'd say 2 to 3 paragraphs. I then also included links to my CV, my
statement of purpose, and a writing sample reflecting my interests and overlapping with the research the professor is conducting.
All of the professors I sent e-mails to replied, though, contrary to science programs, they do not try to establish some further communication, which, in our types of fields, is not necessary, because we're not looking for lab projects and RAs. They will usually reply something along the lines of: Dear X, Thank you for contacting me. Our research interests our similar indeed and I look forward to reading your application material." or "I will read your application material with great attention." And that is the main thing we want to achieve with the e-mail. You might have real questions about whether they'd be interested in your proposed project and such, but the main goal is to get them to remember your name when they have to go through a pile of applications. Of course, make sure to only contact those who's work you're really familiar with, when, e.g;, you've used one of their texts in your honor's or MA thesis.
To give you an idea, of the 16 universities to which I applied, I contacted 5 or 6 professors. Of the 4 admits I received, 2 were from universities where I had contacted someone. My experience is really about 50-50, but I know that for small universities (like Brown) where only few students are admitted (in my program, it was 5 out of 200), they don't want to waste admits on people whom they expect will not attend. But I'm rambling and I've said all of this before; I'm getting a bit nervous for my departure next Sunday...
Too little time, too many things to arrange before...