How do I properly level up my FFX character's stats?

This game is ment to take time. If you want to be able to beat it you must simply fight the other monsters and gain sphere levels then use power, mana, speed, and ability spheres to up your stats and magic/skills.

I suggest you level up ALOT during the game, don't run from battles unless it's nessecary. Try to get all of the sphere balls filled in from the Sphere Grid at a time, try not to jump around with it, you'll be screwed/stuck. Take your time, and level up your characters with what they're best with!! Level LuLu up with magic/healing spells, same with Yuna, level up Auron and Wakka with skills, level up Kimahri and Tidus up with combat skills! And try to fill up EVERY health node in the spheres! Hope this helps!

Try getting a weapon with triple AP, triple overdrive and overdrive=AP abilities on your weapon. You can get a triple AP weapon off a beast arena monster called one eye, after getting one of these weapons with two free spaces, enchant it with overdrive=AP (door to tommorrow X10, get these from the beast arena) then with triple overdrive ( 30X winning formula, get this by bribing a sandworm 20X it's own health if it misses, bribe one more gil). Afterwards, battle the cactuar king monster with the overdrive mode stoic. You should gt lots of level ups afterwards. Hope this helps!

I just run in circles next to a save point for about thirty minuets to an hour.

That's what I do too and my stats are only about 6799 at best and that's just wakka and auron. I jusy don't want to.go through all the trouble of finding all their ultimate weapons

I was the same my 1st playthrough, was very weak, this time however I'm a beast! All thanks to one simple difference; I never ran from one single battle, I went the long way to everything,never used no encounters and just kept fighting every single battle I got into, djose highroad, mihen highroad, oh I spent ages on the bit of straight road in bevelle I think?? Just before you fight seymour hes waiting at the top of the road, but if you just keep fighting the robots next to the save sphere, you get loads of ap. So it's simple, no fleeing, no "no encounters" and fight all the battle you encounter and make use of all them long roads for grinding!