So I earned a new officer when I completed a mission. I selected a science officer, but he isn't showing up on away missions and isn't an option during space battles. So what do I do to use him?

Press "u", which should bring up either your character pane or your ship's character pane. Click on the Assignments tab, and you should be able to put your science officer into both a bridge position and an away-team position. If you can't, check the right side of the Assignments tab...his transfer may be pending, awaiting your acceptance. If he's not there, check your inventory; I had an officer appear there once. If you still can't find him after checking all of those places, submit a ticket in-game...your officer probably forgot to file his paperwork or something (i.e. bugged out).

Thank you! I had to assign him.