MEPS stands for Military Entrance Processing Station, and is where your real qualifications for joining the Army are determined. MEPS is not owned by the Army. In fact, it's not owned by any of the branches. MEPS is a "joint-operation," and is staffed by members of all the branches.
There are 65 MEPS, located across the U.S. Usually, the MEPS process takes two days. Depending on how far the nearest MEPS is from where you live, you may have to stay overnight in a contract hotel.
Unless you already have a valid Armed Forces Vocational Aptitude Battery (ASVAB) score, you'll usually take the ASVAB on the afternoon you arrive. The next day, the real fun begins -- and it's a long, long day. Your day will start at about 5:30 AM, and you won't finish until about 5:00 or 5:30 that evening.
Your day will include a urinalysis (drug test), medical exam, eye test, hearing test, weight check, body-fat measurement (if you exceed the weight on the published weight charts), security clearance interview, meeting with a job counselor, reviewing enlistment options and possible enlistment incentives, taking the enlistment oath, and signing the Delayed Enlistment Program (DEP) contract. Oh, yeah..... intermixed in between all of this you'll fill out lots of forms and do lots and lots of waiting.