Instructions
Use the spells that you do have to your advantage. Purchase a "Final Fantasy 10" monster guide at a gaming store and figure out what each monster's weakness is. If a monster has a weakness to fire, even the simplest fire spell will be devastating. You don't need to use the sphere grid to upgrade to the third level of fire spells.
Run away at every opportunity. Without powerful weapons and spells, your party will be vulnerable to defeat by more powerful attackers. All monsters you encounter beyond the Mi'ihen Highroad may be impossible to defeat for a party that hasn't been enhanced by the sphere grid. Raise your odds of escaping these challenging battles by placing your most agile party members -- Rikku, Tidus or Yuna -- in the front lines of your battles.
Take advantage of the "overdrive" function. Use small skirmishes with weak foes to build all of your characters up to overdrive. Once your characters' overdrive bars are fully charged, avoid battles and save up your overdrive attacks for boss battles or other battles that you can't avoid. Even without upgraded weapons or stats, overdrive attacks can be devastating enough to defeat even the more challenging bosses.