How do you do applications after gap year?

I agree with @clemensd — the easiest thing to do is usually to commit to a school that accepted you this year and ask them to defer the start of your program for a year. That way you don't have to apply again and won't need to go through the whole process of sending test scores, transcripts, etc. all over again (which should also save money).

However, if that's not an option for you then the process is pretty much the same as it is, logistically, as someone applying directly out of high school. The difficulty comes from things like communicating with your high school to get recommendations and transcripts sent (since you're not there every day anymore). If you are re-applying to the same schools you applied to out of high school, whether or not they accepted you before, you should write new essays and a new application — if the same admissions officer gets the same application with the same exact essay a year later (which is likely, since admissions officers usually do the same school or region each year), they'll wonder why you're applying again. If they accepted you, they'll ask why you didn't just commit the year before; if they rejected you and see the same application, then they'll likely just reject it again. You absolutely can apply to new colleges though; there's no rule about that. And some schools in their supplements may ask you to write about your gap year, though honestly if you end up working on personal projects you're talking about, I'd recommend writing your Common App essay about those (it'll probably be stronger).

If you've already applied or started the application process, I recommend just deferring your college start. This way you have your peers and HS counselors to help you through the application process. Also, many people are more comfortable mentally when they know what to expect for their future. Finally, you may find motivation during your gap year if you know its end date. Good luck!