My templar is level 20 and I have unlocked (at 18) the slot for relics. Where do I find these? Do I have to purchase them from a merchant? Crafting? I haven't been able to find anything. I guess another question is what do the relics exactly do?
They are random drops in the game world just like other items. I seem to have found them dropping more frequently as the game wears on.
If you want one earlier, I suggest hitting the auction house. There are plenty available for very cheap.
The relics are just another way to increase the stats on your followers. It works just like an item slot that only the followers have access to.
Another thing you should know about equipping followers is that they receiver a 2.5x multiplier to any of the base stats (STR, VIT, INT, DEX), so it is advantageous to seek out gear for them that maximizes that.
Relics are just another stat increasing gear. They can only be found as a drop from defeated enemies.
Here's a list of some of the different types to be found.