Materia is the most important item of the entire game. Very few people are able to beat the game without them. As you know they are the responsible for your extra abilities such as magic or extra HP. However training these beauties takes time and a lot of patience so I am here to tell you how to make them grow much much faster.
The first thing you need is the double and triple materia growth equipment. Select Cloud, Cid and Vincent as your party members. Now equip the "Rune Armlet" on all characters. Their armor is now growing materia twice as fast. On Vincent equip the shotgun that grows materia twice as fast and on Cloud and Cid equip Apocalypse and Scimitar. Now your babies grow three times faster.
Now you need a very good place to train. You guessed it. The best place to get AP is in the Midel Area. Get the Fury ring to make things easier for you. Now just keep killing those creatures until all you materia goes to MASTER!
Some players prefer to train in the crashed Genilka. However the enemies there are so strong that it will take you a lot of time to kill each one and in an hour you make much less AP than in the Midel Area.