Tactics, basic openings and basic endgames.
You don't need to know how to checkmate with Knight and bishop vs king, but you need to know basic mates (Queen vs King, Rook vs King) pawn(s) and king vs king endings. In some cases you can win, in others you can only draw. You need to know what you must play if you are the attacker and if you are the defender.
No need to learn extremely complicated openings with tens of variations, but you need to know at least some basic openings with maybe a couple variations.
Spanish, Sicilian and Giuoco Piano are probably the most popular openings for e4.
Remember the basic principles of the opening: Center control with the pawns, develop your pieces, castle, do not play the queen way too early.
If you follow those principles you will be Ok in most cases.
And most importantly, solve problems. Try to develop the ability to see winning combinations.
I have a rating of 804 and will be competing in a state tournament soon. So what should I study?