I’ve already discussed how to find a suitable PhD program for you, so I’m going to focus here on how to write a strong statement of aims and purpose (aka. statement of purpose or personal statement).
First, read the guidelines carefully. If it says one-page, stick to one-page. Single or double spaced? If it doesn’t specify, I’d go for a single-space document with block paragraphs with a blank line between paragraphs (just like this “document”). It’s a lot easier to read than a double-spaced document. Use a font that’s easy to read rather than those that look nice but slow down the reading process.
A strong opening statement that grabs the reader’s interest is important, but don’t get too fancy. In my experience, what appeals to the admission committee is not the style of writing (although the lack of style could work against you) but the substance: that you are an intelligent person who is devoted to the field; that you have a clear sense of purpose; that you know enough about the field and are eager to learn much, much more; that you have done the homework to find out about the strengths of the program you are applying to; that you have the determination to complete the course of study; that you are a pleasant person to work with (or rather, that you are not an unpleasant person to deal with).
These are not to be stated explicitly. Instead, they have to come through to the readers as you state your sense of purpose in pursuing a Ph.D. degree.
In other words, voice–“the amalgamative effect of the use of discursive and non-discursive features that language users choose, deliberately or otherwise, from socially available yet ever-changing repertoires” (Matsuda, 2001; see also Matsuda and Tardy, 2007)—is crucial in this type of academic writing; it is inseparable from the substance.
It’s also important to have a sense of what you wish to do when you complete the course of study and why you think the program you are applying to can prepare you for that professional goal. Is it the scope of the program? Is it the particular set of courses that are available? Is it a specific faculty member (or faculty members) who has the theoretical and methodological expertise that you are interested in acquiring?
In the process of preparing the document, you will (I hope) find out a lot about the program you are applying to, which will help you develop a realistic sense of what you can expect from the program. I also hope you will learn more about your own reasons for pursuing a graduate degree and how much you really want to study in that program. The opportunity to examine the match between you and the program of your dream might be the second most important function of the statement of aims and purpose.
The most important function, of course, is to get yourself admitted to the program.
Good luck to you all!