You are given 13 tiles, and your objective is to make 4 sets and 1 pair (generally speaking). So you can have [1-2-3], [4-5-6], [7-8-9], [4-4-4 of another suit] and then two blank white tiles, for example. If you've ever played Rummy, the playing card game, it's very similar to that where you build patterns.
Some patterns are worth more points than others, and MahjongSoul increases the odds of
players drawing tiles that allow them to go for the really rare and exciting patterns, or creates scenarios where
people get completely fucked over.
Each turn, everyone draws a tile from the Wall, and discards a tile in front of them as they build. The strategy comes from knowing what tiles other players are looking for based on what they're discarding, so you know what tiles are safe to discard. If you discard a tile that a person needs to win, they can declare 'Ron!', and the points their hand is worth is deducted from your Life Points and added to theirs. If their winning tile is pulled from the Wall, they declare 'Tsumo!' and the value of their hand is deducted evenly across the other three players and added to them.
Naturally, it is a game of trying to drain others of their points quickly and not giving them an opportunity to ruin your day. There are a lot more rules but that's the gist to understand what you're looking at on screen.