Chinese mahjong is a bit more liberal with how you can win. Really though the rules vary all over the place even within the country.
Basically how it works is like this: You have 13 tiles in your hand and must complete a hand of 14 to go out. You can only hold 13 unless you are winning on the 14th which is why you always discard one.
Generally you need some combination of chows & pongs to win (combination-of-3 sets), with a pair of something tossed in so you can make 14. If you get a kong notice that you draw an extra tile so you still have the same number as if it were only a pong.
Ignoring all the special hands like Gates of Heaven (which I have done, and it's hilarious to watch what happens to the opponent) you beat them depending on the strength of your hand which I think the booklet explains, or at least lists in ascending order.
So say 3 pongs and a chow + a pair, you win.
Kong & 3 chows + pair, you win.
2 kongs & chow + pong & pair, you win.
etc.
In Japanese mahjong though there are some other rules.
For one thing they don't seem to use flower tiles. You can also declare REACH in Japanese mj which means you are 1 tile away from winning and you announce this. In doing so you also bet 1000. If you declare REACH and win you get bonus points. If you declare REACH and your opponent wins, bonus points to them. If you both do and one of you wins, more still.
Stalemate is when you both run out of tiles to draw. You both show your hands in that case. If someone is only 1 tile away from winning that is TENPAI. If they are more than one away from winning, that is NOTEN. TENPAI prevails over NOTEN. If someone declared REACH and it's a stalemate that concludes in a draw (double tenpai/noten), they lose their 1000 (does not go to the opponent), else it goes to the winner (the one with tenpai).
So then, adding more confusion to it, in Japanese mj you can only declare reach if you don't use any of your opponents discarded tiles and if you do use any, you need to have a pong of kong of bonus points as I understand that (winds or dragons).
Minasan cheats so badly it's not funny. It gets a bit more bearable when you learn all the different combinations of hands that can win and see that victory is not necessarily as far away as you might think.
Keep in mind a few pointers for higher score too:
winning with no tiles showing = more points.
winning with all one suit (+-bonus points) = more points.
special hands (see the mahjong guide) = more points.
reach can be good for extra points though be cautious about it.
Always note what your opponent is discarding since it will likely reveal some idea of the hand they are building.
And particularly for videogame mahjong, don't put all your eggs into one basket! The items are very useful and even more addictive. Just don't blow them all in one round! While in some games this works wonders often times the Minasan AI will give you a KILLER hand except for the fact that you must discard one tile which (if you have your X-ray viser on) you will see is the one the computer is waiting on to win with some cheesy shit hand, and there is simply NOTHING you can do about it. You have to take some losses like that and expect these to catch you off guard. Also if using the X-ray, make certain you keep a watchful eye on what your opponent needs to win. In haste for your own winning tile you can very accidentally give them just what they want.
Don't be afraid to let it run to stalemate, sometimes the best thing you can do is merely to stop your opponent from winning. This is especially true and even harder to control in 4P mahjong -as the game is intended to be played. As the Nine Dragons site says, sometimes destroying your hand to stop other people winning is the best thing you can do.
And finally Minasan has unlimited continues (bless Jesus!) so you can spend all afternoon at it and never have to start over, unless you get your ass kicked all the way back to the beginning which can and probably will happen at some point.
If you have a debug BIOS try switching to MVS mode and lowering the difficulty or something, it's fairly high on the homecart as with all the oldest games.
.