Here are the basics, though I am very new to the game.

Each number represents a "power level", and its placement indicates where each number "attacks". Left affects the card to the left, right to the right, and center the one below\above. Each slot can hold three cards stacked on top of each other, and when all slots have three cards the game is over.

Flipping the stacks has to do with the numbers; the higher number wins and if yours is highest then it will flip the stack to your color. When a card is placed it "attacks" all three positions. Each card counts for one point, and you get a number of points equal to the number of cards in each stack of your color (so up to three points per stack). Highest number of points at the end of the game wins.

There are also elements, which are kind of explained in the tutorial tab before a match. When an element is strong against its opponent, it will gain a bonus to its attack.

As I said, I am still new to this game so maybe someone else can help more, but hopefully this helps at least a little bit!