It is mostly depending on where you're located. But be ready for a lot of waiting around. I joined in Puerto Rico so, I showed up to the MEPS early morning, about 0500-0530, they didn't make us stay in a hotel or anything like that. Sat in a room before been called by an admin clerk to start the final paperwork such as orders, plane ticket or bus. Some say they do another physical, but I know you'll do a drug test, and weigh in. You'll get handed your packet, then wait until everyone is done so you can all sworn in together before getting in the bus. But, just be ready for a very long day.
Same process as before but minus all the examinations, you go into the office of your branch and you finalize your orders and you sign the contract, after that you go into the ceremony room where you swear in again if you're active duty, if you are going reserve, you don't swear in if I recall, after that you watch two videos about what happens from here on out, and what to expect. Then you get your envelope containing your orders and records and airline or bus ticket, then you kiss your family goodbye and it's on the bus or van to the airport or bus station where from there you will begin your military career. Good luck.
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