At level 15, you'll be able to start dying your gear different colors! The quest is called "Color your World" and is given by Swyrgeim in Western Thanalan (The footfalls- Vesper Bay).

At level 50, you will be introduced to "Glamours" which enable you to make your gear look like whatever you choose. You can pick up the quest "A Self-Improving Man" from Wisecard in Mor Dhona (X:22, Y:6).