During your time in MO NROTC you will be given a chance to pursue an "Aviation Contract". Some contract earlier than others, your det will know the details. You will need to take the ASTB as stated and score high enough to qualify (see below). Your scores and package will then be sent to be a board to be selected. Its usually not that competitive, but you never know year to year. There are study guides and online stuff to help see where you stand on scores and improve. You will not get a fixed wing guarantee, just an aviation contract. Once you complete TBS, then you will be sent to flight school. At flight school you will put in your list and then be assigned a platform. Airwarriors is an aviation specific forum that lots of Naval Aviators participate in, but can be pretty harsh, so do your homework before posting. Also, Hurricane12 is a USMC Pilot from USNA. I am sure she can provide details too.
Minimum ASTB-E scores for Marine Pilots and Marine Flight Officers: 4 AQR, 6 FOFAR.