http://www.ffxivinfo.com/materia/guide.php

>>>After completing the Life, Materia and Everything story quest you can unlock materia melding. You will be sent to The Bonfire in Central Thanalan at 23,13 on the map and told to speak to Swynbroes. He will give you the "Forging the Spirit" quest.
Upon completion of [Forging the Spirit] you will receive a key item called a Materia Assimilator. This key item will allow you to create materia when certain conditions are met. <<<

There's a second quest that you have to do (Forging the Spirit) in order to actually create Materia. You need to have a level 19+ crafting class in order to accept this quest.