This is the simplest way I could help you. Just so you know, I'm not articulate in explaining and If I didn't help, watch videos on it online or play to understand the mechanics better. So to win at mahjong, you need 4 sets and a pair. A set is 3 tiles with sequential numerical order(EX: 1,2,3) or 3 tiles with the same value. A pair is two tiles that are the same. Basically, you need 4 sets of 3 tiles and a 1 pair of 2 identical tiles. If you think you need one more tile to win, mash the square button for Riichi. I tried explaining it the best I can.
I understood better through playing, watching videos on mahjong, and people explaining it to me.
P.S: You'll need to memorize the character tiles and the other tiles(specifically, the dots and the bamboos)to know their value.
By the way, you seemed to finish the Climax Battles. Can you explain how to do Proving Grounds 1-8 and Melee 3-6?I'm having a hard time with them.