I see we still get newbies who are stumped on the blitzball tournament. The odds are tilted against you, but a little bit of strategy tilts it back in your favor, and you don't even have to use the cheat*...
Here's the key -- ABUS (RF) is a lousy defender, while BALGERDA (RD) is mean mean mean and will take the ball from almost anybody. She's guarding Tidus, if you leave him at his default position (LF).
So send a ball carrier to the wall to draw defenders away from Tidus, clearing him to shoot:
Once you've scored a couple, pass the ball back and forth between Aurochs to hold the lead.
I've got a few other tips on this blitzball guide page, but that should do it.
*I've heard if you hide behind your own goalcage, the opponent ignores the ball carrier. I haven't tried this.