I'm interested in becoming a fighter pilot in any of the three branches that have fighters. How does that process works?

Your best bet is to talk to a recruiter

Have good fitness scores, solid health to include vision, and be well on your way to a college degree. Besides that you need to be talking to a recruiter to get the details and get started

Ari Renold As mentioned by SSG (Join to see), you need to talk to a recruiter. Before you do, research the military branches to find out what each has to offer and what the requirements are to become a pilot. Many of your questions will be answered by your own research, so you will have focused questions to ask a recruiter.