There is no single "correct" way to do it, no formula. However, strong statements usually incorporate some or all of these elements:
- We are interested in you as an individual! We love to hear about what questions excite you, what your plans and hopes for the future are, what experiences have informed your thinking, what you hope to learn in graduate school, what makes you happy… play to your strengths and your passions. If you are invited for an interview, you'll have the opportunity to have one-on-ones with grad students and post-docs who are excited to learn about you in a non-evaluative capacity.
- Identify a few faculty you'd like to work with, and describe how you can see yourself engage with their work. Show that you have taken some time to get a sense of what they are doing and how it fits with your interests and goals. You are encouraged to contact specific faculty members to find out if they are taking new students, and so that your name is on their radar when reviewing applications. See below for some tips on writing a good introductory email for this purpose. (This step is especially important if you don't select that person's name as one of the top 3 faculty you are interested in as part of the online application, because some faculty only review applications they are listed on.)
- Research experience is often helpful: if you are going to be doing research for ~5 years, how would you know if you'd enjoy it? It is however not required to apply: there are many paths into brain sciences, including from engineering, computer science, philosophy, and vocational training, in which research experience is not common. Some outstanding scientists didn't get formal research experience opportunities until later.