Here is the offical Navy rules for striking for a rating....
I am guessing you are in UNDES school or on leave.
Once you get you to your first command, you will meet with your CCC and COC, they will show you what you are qualified for. While you are on board you will be assigned one division to work in, but if you want to go see what the other division do you do that on your off time.
After you have been on board 12 months you can request to go to an "A" School. IF there is an opening. than you request an "A" School, BUT that doesn't mean you will get it as there are limited openings.
If you get to E3 and you are eligable to take the exam, you can reqest to take an exam in some rates. Not all rates allow you to just take an exam. BUT again, that doesn't mean you will get approved to take the exam, there are only so many openings for people to take the exam.
Al the information to see what is open for either getting to school or taking the exam is in a program called FLTRIDE which the CCC has access to.