Artifact Weapons in World of Warcraft: Legion are easily one of the largest additions to ever come to the game as a whole. It is incredibly important to strengthen your weapon as powering it up adds tremendous bonuses and effects to your entire character. Unlocking traits on artifacts require an XP currency known as Artifact Power (AP) which can seem less than abundant, especially when the weapon starts requiring over 10K AP to level up. But finding AP isn’t as difficult as you might think when you know what to look for and where.
All Artifact Power that is generated for your weapon comes from consumable items that add different amounts of AP (depending on the item). Right when you step foot on The Broken Isles, AP items can be found from chests and rare encounters. Chests are littered all around each zone in The Broken Isles, but can sometimes be difficult to find. They come in three sizes: small, standard, and large. The larger the size of the chest, the more likely you are to receive a higher granting AP item, but you will always get an AP item of some sort per chest you open. Rare encounters are special monsters or side quests that appear in The Broken Isles which generally require you to kill a higher-than-normal hp enemy. Rare encounters are fairly easy to spot as they appear as stars on your mini-map when you run past them, however not all rare encounters will drop AP items.
Upon reaching level 110, you will also unlock the ability to complete daily World Quests. A large majority of these World Quests will reward the player with a high granting AP item, especially if it is an Elite World Quest (blue quest marker with a dragon around it). Queuing up for random Legion dungeons in the Dungeon Finder is another great way to farm up AP, especially when doing Heroics, as a heroic random dungeon will award 400 AP. Finally, for the PvPers out there, completing Battlegrounds or doing randoms will also net you AP items as will attaining specific honor ranks in your Honor Talents.
Eventually, you will hit a roadblock in your Artifact Power gains where the AP you are getting seems incredibly low compared to what is required to level. This is totally normal and Blizzard has given us a way around it. In your Order Hall, you will have the ability to create Artifact Research Notes. Upon use, these will permanently increase the amount of AP that items give by a certain percentage. You will be able to use 25 of these items, but be warned however, as it takes 500 Order Resources and 5 days per Artifact Research Notes you create (with a max of 2 being created at a time).