The Armed Services Vocational Aptitude Battery (ASVAB) is developed by the Department of Defense and offered by the US Military Entrance Processing Command. The ASVAB is available at many schools and Military Entrance Processing Stations (MEPS). There are 65 MEPS located in the US and Puerto Rico. You can look up the various locations at this page.
Depending on the version you take, there are about 10 sections to the ASVAB. There are four sections that are particularly important. The Arithmetic Reasoning, Word Knowledge, Paragraph Comprehension, and Mathematics Knowledge sections go towards your Armed Forces Qualifying Test (AFQT) score. The AFQT score determines whether or not you are qualified to enlist. To join the US Army, you must have a score of 31 or more on the AFQT. The other areas of the ASVAB will determined how qualified you are for various Military Occupation Specialties (MOS) and enlistment bonuses. For more details about how the ASVAB helps to determine which MOS is right for you, please look at this page.
There are numerous commercial study guides and test aids available online, at local bookstores, or even the public library. You can take two practice tests on Army. - Test 1 and Test 2 - that use questions like what you'll see on the official ASVAB.
State employment service offices frequently will offer adult education programs that are beneficial. The US Army has also developed an online program to help you refine your basic skills -- March2Success.
Bring valid identification with you or you will not be admitted to the ASVAB. If you are late, they will turn you away and you will have to reschedule the test.
There are actually 3 different versions of the ASVAB: