Get yourself into the right state of mind before starting the application process. Think of it like taking an important test. You should be well rested and well fed. Remove yourself from any distractions; choose a quiet, well-lit location with a clean workspace and a comfortable chair...and turn off your cellphone. Bring a snack and a bottle of water, particularly if you're filling out multiple applications.
Fill out the basic information fields on your application. This includes your personal information: name, mailing address, physical address, citizenship status, ethnicity and so on.
Fill out the family information portion of the application. Typically, you'll need to give the names, addresses and levels of education of your parents and siblings.
Provide your academic information. You'll need to fill in the name and address of your current educational institution, the date you'll graduate, your counselor's name, your course load for the current academic year, AP/IB test scores, SAT/ACT scores and a list of your extracurricular and volunteer activities. You should also supply any academic distinctions: awards, honors and/or any involvement with the National Merit Scholars or National Honor Society.
Write your personal statement. This is going to be, by far, the hardest part of filling out your application, but don't be intimidated by it. Many colleges will give a fairly broad writing prompt to give you a framework upon which to build your essay. Typical prompts ask you to give examples of how you triumphed over adversity, why you feel you're a good fit for the university, what life-changing experiences you've had and so on. Do your best to write clearly, concisely and comprehensibly. Have a teacher or guidance counselor look over your essay before submitting it.