Choose the Best Equipment
Materia equipped into your weapons and armor gain the AP that you earn from a victory. Each weapon and accessory allows for a certain number of materia slots, and many pieces of equipment multiply AP gained for any materia equipped within them. Cloud's Apocalypse sword, for example, holds only three materia but triples the AP for the materia equipped in it. Similar examples include Cid's Scimitar for triple growth, and any character can equip the Rune Armlet for double growth. Every piece of equipment shows its AP growth rate for materia, so equip materia according to your goals.
Farming AP
AP gains vary for different enemies, so grind for AP in areas with enemies that yield high amounts of AP. Toward the end of the game, visit the Northern Crater for two particular enemies; "Magic Pots" and "Movers" yield 1,000 and 800 AP apiece, respectively. Note that Magic Pots only take damage after you feed them elixirs.
Boss Battles
Some of the best AP gains come from boss fights. Use the opportunity to equip your party accordingly prior to boss fights for optimal AP gain and materia growth.
Ultimate Weapons
Every character can equip an "ultimate weapon" in the game which holds eight materia slots, but beware: these slots grant no AP growth to materia whatsoever. In general, equipping characters for AP grinding means using less than the best equipment for winning your battles.