What should I study and/or learn in order to succeed in a promotion board appearance?

Most people will tell you study the items on the MOI, which is not wrong. However, I will tell you from competing at several boards all the way up to the Pentagon, and sitting on boards, you make or break your appearance within the first 5 minutes.
You should practice your reporting procedures, marching, and rehearse your bio, as well as any Creed that you need to know. For instance, when I was at 3rd ID you had to recite the soldier Creed, the NCO creed, sing the dog face soldier song, and the Army song before you sat down and spit your bio. When you are rehearsing your bio practice projecting your voice. When I have soldiers do a mock board I sent their chair as far away from the table as possible so they have to get into the habit I'm speaking loudly for the board members to hear.
If you look at the grade sheets only half of the proceedings judge your knowledge. The other half is uniform and appearance and Military bearing.
When you are prioritizing what information to study first, study you're unit history and current events. Typically, the board president is the one who asks these two questions

If you are going to present at an In Person board, then you should receive an MOI (Memo of Instruction) that explains who will be on the Board, what each topic the Board Members will ask you questions from, the time and location of the Board, the uniform in which you will be in, etc. This memo should also provide instructions if you need a sponsor or not and what instructions the sponsor needs to know (if any). No matter the uniform you are to appear in, ENSURE it is the best and most squared away uniform on the planet. Chances are it will be in your ASUs so go over that uniform with a fine tooth comb, ensuring that everything is where it should be, at the right measurement and free of stain. Have someone quiz you every day all day from the topics the MOI gives. Also, have your Bio written. The MOI should give explanation on this, as well.

Definitely study what’s on the MOI but also practice the confidence that you have when delivering the answers for the board. You can’t and won’t memorize everything so the advise that I have been give is study the questions that have dates and lists for answers. If you don’t know something, tell them but have confidence in it when saying it. “CSM, I do not know CSM but I can get you that answer CSM.” Your appearance, marching, facing movements all must exude confidence as well. Show that you are professional at all times. Even if they laugh at you, don’t laugh with them. Remain the professional NCO that you are. The Creeds, know them and sound off like you’re never sounded off before. Speak with creeds clearly and drink the kool aid a bit. Have some umph with someone of the words. “ I AM an American Soldier. I am a WARRIOR and a member of a team.” Let some of the sentences linger. Don’t just sound like you are reading the words but mean them, like them and love them and again...... SOUND OFF! Sometimes you can get away with just sounding off and sounding like you are the proudest Soldier to walk this earth. Have a great story. Really tell your story. Try not to do all of the “ummmmmm” or “ uhhhhhhhh”. No one knows your story better than you so let it flow. Don’t talk with your body or your hands. Sit at the position of attention and make eye contact. Again, all with confidence. Have as many mock boards as possible. They help a lot. Don’t be afraid of harsh criticism. This is only to set you up for success because you will be representing your sponsor as well.