You contact a recruiter, and provide evidence of your citizenship or perminant residency (birth cert. or ‘Green card’), academic qualification (HS diploma, GED, University degree, etc.), and any applicable medical records (for thing like busted bones, etc.).
The recruiter interviews you, to refine you qualifications, and will check your crude physical quals by checking your height/weight, interview IRT things like sleep walking, bed wetting, bolts, pins, plates, screw, asthma, and other conditions. He or she will also likely give you a screening ‘pre test’ for the Armed Services Vocational Aptitude Battery (ASVAB), to get a rough idea of your placement scores - Unless you already have a valid ASVAB score on the records (and they will know if you do).
Presuming you have no obvious disquals, and haven’t taken an ASVAB yet, there will be some preliminary paperwork to be filled out, including an SF 86 (Background check), which will be sent off to various agencies for police record checks, and you will be scheduled for an ASVAB test.
Presuming you get a ‘good’ score (i.e. one that matches up with the needs of the service), you’ll be scheduled to visit MEPS (Military Entrance Processing Station) where you’ll be interviewd some more, take a physical, and fill out some more paperwork.
Presuming you get a passing physical, and have no disqualifying factors (serious police record, un-satisfied judgements against you, probation, belonging to a violently radical group, etc.), you’ll then sit down with a classifier, whom will look at your scores, your desires, and the needs of the service, and negotiate with you the job you’ll sign up for, and when you’ll ship out.
After visiting the Classifier, you’ll do still more paperwork, preview your contract, and swear in (for the first time).
On shipping day, you’ll again go to MEPS, fill out yet MORE paperwork, swear in a second time, and get your butt on the bus.
IF you have medical issues, you may instead be sent to MEPS for a ‘consult’ visit, where the docs will look at you and determine is 1) you can qualify, and 2) what kinds or records you’ll need and / or what kind of specialists you may need to see, to determine if you are qualified. Any specialist visits will be schedlued (at no cost to you), and you’ll be given date(s) to show up for your consults.
Mind you, this is a general description, and not even remotely as detailed as it could be -there are multiple services, and each does things slightly different. I recruited for the Nav, and know their procedures the best. When I came ‘off the bag,’ only roughly one potential applicant in four was mentally, morally, and physically qualified to join any of the services. That’s right: 75% of the target population was unfit to serve. If a recruiter comes knocking, and keeps coming back - consider it a compliment of sorts.