Okay, let me try to explain as best I can what I've figured out. I don't speak a word of Japanese either; this is all guesswork.
You have to get 3 of a kind to win a point, so to speak. You have to be the first to get 5 points to win the match. When you win, you get to tickle the girl who had the least points in the match - which means sometimes you get the same one several times in a row.
Now, if you notice the little 'point' icons (near the top of the screen, they look like an animal print) sometimes they will be lit up and sometimes dark. Whether they are lit up or not depends on how fast you win the point. A draw is declared after each person goes six times and no one gets the point. If you get all 5 points to be lit up, you'll face the "boss" girl in a one-on-one match. Obviously you get to tickle her when you win, as well.
If you win and claim your tickle reward, when you go back to the "menu" screen you'll see buttons at the bottom of the screen. The button on the bottom right lets you tickle girls you've already defeated in the card matches for free. The button on the bottom left appears if you've unlocked the boss character - you can toggle a normal match or the boss match with that one. The other two are just rules and profiles type thing, basically useless if you can't read them. Anyway, that's about the size of it, I think. Good luck - sometimes the computer is tough to beat. 😛