Many high schools give students the opportunity to take the ASVAB as part of career exploration. If you chose not to take one in high school, then you will have to schedule a time to take it. You can contact the Armed Forces Recruiting Officer in your area and you can schedule an appointment with a local recruiter from the branch of the military you wish to join.
The Armed Forces Tuition Assistance (TA) Program allows enlisted servicemembers and offers to enroll in courses at accredited colleges, universities, junior colleges, high schools, and vocational-technical schools. TA will pay up to 100% of the cost of the course and up to 100% of the cost of obtaining a high school degree, with a limit of $250 per credit hour and an aggregate annual limit of $4,500. MGIB benefits may be used to "top up" TA benefits, paying the difference between tuition and the TA benefits. Military.com provides a good overview of the tuition assistance program.
A good score on the ASVAB is different than a minimum required score. Each of the military branches will have their own minimum required scores (see below). In practice, however, each branch will be more selective in their recruiting. A score of 50 on the ASVAB implies that you scored as well or better than 50% of comparable test-takers. Since ASVAB scores are used for many purposes (e.g., enlistment eligibility, military job placements, and career exploration), it is important that you score well on the ASVAB. A score of 60 or better should be your minimum target.