Umm, I think you can find some quick details here.

Basically, you fight one eye in the monster arena to get his weapons, set your overdrive mode, and fight Don Tonberry. You can find really good walkthroughs at gamefaqs.

Some people thinks that takes a long time. It only took me about 1-2 hours to start reaping some moderate benefits. You dont' really need any of the overdrive bonuses or AP bonuses. You'll do OK with just the weapons from one eye with overdrive -> AP.

If you are feeling really lazy, just go whoop some at the Omega Dungeons. Thats a good place to get some quick levels.