Because I was a student at both the Northlands and Loring Centers, I am intimately aware of the process.
Basically, you will meet the admissions counselor first. If you're an adult the job office will be where you can get the contact info. If you're in high school, or if you have a student who is in high school, the guidance counselor will have this information.
When you meet with the admissions counselor, who will tell you everything about the program and about what is available at whatever centers they have access to, you will fill out your paperwork and choose your center.
The admissions counselor may push for you depending on your attitude during the meeting. Depending on which center you go to, you should recieve a phone call from that center about a week from your meeting. You'll be asked a ton of questions like how much time you plan to commit to the program, what are your career goals, can you commit to doing your chores, getting up on time, etc.
The person who calls you may be in charge of student life. After that person talks to you, you may also be called by the person in charge of what dorm you'll be sent to. (Most Job Corps centers have a specific dorm for "newbies")
Then they will determine how to get you to the center as fast as possible. This could be by bus, plane, train, etc. They will send you the ticket via Fed-Ex and after that it's up to you to get yourself there.