In this guide you will learn how to complete any prophecy in Path of Exile. It is currently a work in progress, so if you don't find the prophecy your looking for, it will be added at a later date.
The Unbreathing Queen I: This will trigger once you travel to The Fellshrine Ruins in Act 2. The spectres can spawn at any location in the area, but if you want to just get rid of the propecy, you simply need to travel to the area to trigger it, and you can get a new one.
The Soulless Beast: You need to kill an enemy known as Ancient Construct, which is found in the Vaal Ruins. The fastest way to get there is by using the waypoint to The Wetlands, which is very close to the Vaal Ruins entrance. The Ancient Construct can be tricky to find, but the prophecy will not complete or trigger until you kill it.
Upon killing it, it will drop Atziri's Foible Paua Amulet, which is generally not worth anything.
A Regal Death: To complete this prophecy you need to kill any boss that has Queen or King in their name. The fastest one is The Bone Queen. She is located roughly halfway trough Belly of the Beast level 1, and just follow the mobs named Bonewarped Warrior to find her. Upon death she will drop a Regal Orb and complete the prophecy.
You cannot recycle this prophecy by entering the area only, so you need to actually kill the boss to complete it.
The Beautiful Guide: Just use a Cartographer's Chisel on any map to complete this prophecy. This is usually worth a few chaos orbs, so it might be worth sealing.
Bountiful Traps: This prophecy will trigger upon creating a map, so to recycle or spawn it, just keep running maps, or even reload maps into the Map Device. There is no need to enter the map, and you can check if the prophecy disappears from the tab (which means it had spawned in the currently spawned map).
This tend to be worth 3-5c, so consider sealing it for profit.
Thaumaturgical History II: Travel to The Western Forest in Act 2. You need to search for a lore piece called Proclamation. Click on it and a group of enemies will spawn. The prophecy will be completed once these mobs have been killed. The Proclamation tends to be pretty close to the main road going south from the waypoint, so it should not take too long to find.
Custodians of Silence: This requires you to kill a rare Assault Ribbon in one of the following areas either The Battlefront or The Solaris Temple Level 1 or 2. You need to actually kill one of these to complete the prophecy, so no easy recycling here.
The fastest way is to go to Solaris Temple and rush trough it until you find a mob that triggers it. Loot the Tear of Purity (it is generally worthless) if you want it, and it is completed.
Nemesis of Greed: This prophecy can be pretty tricky to complete. In order to do it, you need to slay a monster with the Inner Treasure mod, which is one of the Nemesis mods available. So you need to run maps that have monsters with the Nemesis mod until you find a monster with the Inner Treasure. Killing that will trigger a unique drop. The unique item will not be the same as the other that drops, so this can potentially give you a very nice item.
The Plaguemaw II: To trigger and cycle it, just use the waypoint to The Crypt in Act 2. If you want to complete it, search for the mobs which are located somewhere in that area.
From Death Springs Life: To complete this, you need to kill a rare (yellow) Dripping Dead. It will drop a Lifesprig upon death, and trigger the prophecy to complete. The Dripping Dead mobs can be found in The Mud Flats, The Fetid Pool, The Submerged Passage or The Flooded Depths in Act 1.
The God of Misfortune: Travel to The Ledge in Act 1, and head towards the direction in which the three little stones next to the waypoint points. This will take you to the two totem bosses that spawns, and kill these to complete the prophecy. The totems drop a few Orbs of Fusing upon death.
Rebirth: Just slay regular monsters, and this will complete fairly soon.
Hunter's Lesson: This prophecy will complete when you kill a rare monster. It might not be the first one, but you will get it pretty quickly.