There isn't necessarily a right answer in terms of when you should start the application process. Ideally, you should be thinking about college throughout high school, choosing courses and extracurriculars that will set you up to be a competitive applicant, researching and visiting schools in your junior year, and preparing for the SAT and/or ACT before the start of your senior year.
Budget Based on Application/Admission Type
As for completing the application itself, the advice is always to start early, and this has been echoed by many parents and students on The Princeton Review's annual “College Hopes & Worries" survey over the years. The more time you give yourself to craft a strong application, the less stressed out you will feel and the more options you will have if something goes unexpectedly off the rails.
If you are completing the Common Application, you can start working on it as early as Aug. 1. (Note: Often, the Common App will announce new essay prompts beforehand so you can start drafting your essays even earlier.) If you are applying for financial aid, you will be able to start the FAFSA as early as Oct. 1. College application deadlines vary, but typically Early Decision deadlines fall in early November and Regular deadlines fall in early January.
If any of the colleges on your list have rolling admissions, applying as early as possible can help give your application a boost. Rolling admission means that applications are accepted over a few months, and admissions decisions are made as applications are received, instead of all at once following a cutoff date. So there are a lot more spots open at those schools early in the application timeframe than there will be closer to the final deadline.
Allot Time to Gather Extra Materials
Another good reason to begin preparing your application materials early is that you will need to rely on other individuals or systems to obtain some materials, and this can take a bit of time. Your high school is processing requests for academic transcripts for all your peers applying to college at the same time, so confirming that your transcripts have been sent may take a few days or weeks. If you have concerns about your standardized test scores, you may want additional time to prep for and retake the SAT and/or ACT, and like transcripts, your official score reports will take a few weeks to reach the colleges where you're applying.
Once you've completed the FAFSA, and the CSS PROFILE if necessary, the official analysis of your financial information can take up to four weeks before it is provided to your schools. And don't forget about letters of recommendation: You should give your letter-writers at least a month to draft and submit your recommendations, especially if you know they are writing recs for many other applicants.