The Ancient Reliquary Keys are only found in the Legacy Legaue, and they are used to open portals to the Ancient Reliquary. In there you will find a large chest containing one or more Legacy items. These are all items that has their original stats from before they recieved a makeover at one point in the game. Some of these Legacy Items are considered the most powerful items you can get your hands on, such as Legacy Kaom's Heart, which is worth several mirrors!
Anyway, to get the Ancient Reliquary Keys, simply play the game. They can drop at any level, from any mob, just like most currency items. Their rarity is about the same as an Exalted Orb, so they are not very common to find.
You can of course buy them from other players, and their price is around 40-50c per key. However, most items that drop in the chest are considered to be pretty bad, and you likely won't make your money back by purchasing these keys. But if you love to gamble and get some nice items, have fun!
Once you have a key put it into your Map Device to activate the portal. Only the owner of the key can open and loot the chest, so don't worry about being in a party. Once you have the portals spawned, just go to the chest in the large room to loot the Legacy item.