How do I start a personal statement for grad school?
I would start with a brief but relevant paragraph about your field of study, why you think it's relevant and then say why you want to pursue study in this field.
For example, if you're going to grad school for political science, talk about the importance and ideological affect politics has on all aspects of life and your own approach is to deconstruct the polarities (left/right) of politics and how you think it has stagnated political debate (my own jab there).
Then go on with how you got interested in politics, what activities you do related to it: anything from conversations, voting, polling, campaigning, etc. Activities can only help.
I'd also include how/why you're passionate about the subject and what you plan to do as far as career (even if you're still open as to what you really want to do with the degree). You could also just get as specific as mentioning particular areas you're interested in. Professors, even if they are very open-minded, like students to have some kind of vision or plan: not so much for a career but for your own sense of what you'd like to study and that you can show you've already done some work outside of the required undergrad reading. Because you will do more work in grad school than what's required if you want to succeed with flying colors.
Last thing I'd say is to talk about yourself a bit, but focus mostly on the academic vision. If you have a personal story(s) that contributes to the WHY of you're going to grad school, put it in there but it has to be relevant. This is a PERSONAL statement but also somewhat of a business proposal, so it has to be both personal and professional.