Just to make it clear before I start, I am on a PC, but I use a gamepad and the crossbar to play the game as I find that an easier method of gameplay.

Time: 12PM BST
Frequency: Always happens when I get a new spell or skill from an NPC
World name: Shiva
Character name: Cuvelia Stellarum
NPC name: Any NPC who gives quests to learn magic
Monster name: N/A
Class/Level: So far, witnessed it happening on Black Mage, White Mage and Bard
Party or solo: Solo
In-game time: 6:00PM
Area and coordinates: Numerous places depending on where the quests take me
Steps:
1. First of all, you need to level a crafting skill high enough so you can unlock the materia melding command.
2. Find a class/job which you have interest in levelling up and find an NPC who provides a quest for that particular class/job with magic or a skill as a reward.
3. Complete the requirements necessary to pass the mission and speak to the NPC again to obtain the magic or skill.
4. After the initial animation, the materia melding skill should appear on your crossbar. For me it always appears on the L2 + D-pad right slot.