Ancient Vessels are one of the collectibles in Horizon and are relics of the past, or Old Ones. They are essentially cups/mugs with various designs on them and can be found in scrap piles, similar to something like a Scrapper pile. One surefire way to know you found the right pile is that there will be a purple marker above the pile, similar to the loot markers you see whenever you know an enemy has items. There's a total of 12 Vessels in the game, with four being in each set. Remember that you can purchase a map that shows you the general locations of all of the Ancient Vessels in the game.
1) Faro - Southwest of Brightmarket is a Sawtooth Site marked on your map, which is not too far from the cliffside. Just a bit southwest of the Sawtooth marker is a ruined wall with a zipline attached to it. The Ancient Vessel will be at the base of this ruined wall.
2) Arches - Go to Devil's Thirst and you'll find this collectible southwest of the place's icon. Within the search radius given to you, head to the southwest edge of the perimeter and look on the southern side of the river there. You should see a small ledge jutting out, with some debris you can search. You know you're in the right spot, as the debris will have a purple icon; the Ancient Vessel is in that pile.
3) DroneHop - Found just west of the Devil's Thirst Bandit Camp. From the bridge that leads into the camp, follow the road south a bit and the purple-laden debris pile will be on the eastern side.
4) Wayfarers - From the Devil's Thirst Vantage Point, go northeast/north until you find the main path. Follow this north and you should see a debris pile with a purple icon on the side, which contains this Ancient Vessel.
5) Miriam - From the campfire you used to rest at the Revenge of the Nora main quest, follow the main road to the east, passing underneath a large ruined building. The Vessel will be along the main road, in a debris pile, just to the left of the icon on your map.
6) USRC - From the campfire you used to rest during the Revenge of the Nora main quest, follow the main road to the east, past the cultist camp, until it splits north and south. Go south and at the next split, head west to find the Ancient Vessel in a pile not far along this path. It is just south of the vessel icon on the map.
7) KZ - Head south from the USRC Ancient Vessel and you should spot some Corrupted Scrappers off to the east. From where they are patrolling, go straight south and look for a square archway of sorts, which is housing the scrap pile with this Ancient Vessel. It is a little bit west and very slightly south of the vessel icon on the map.
8) Sterling-Malkeet - Located on the southern side of the Shattered Kiln Bandit Camp. It's easier to clear the camp before you loot it, although it doesn't matter.
9) Odyssey - In the pit where you fight the cultists and other enemies after tracking Olin during the main quest, The City of the Sun.
10) Metallurgic - In the northwest corner of the map is the ruins of Maker's End, which you will visit during the main story. Just a little southwest of the ruins icon is a campfire. Go to that campfire and not many steps north of that is the debris pile with this Ancient Vessel.
11) Jomei - During the main quest, The Field of the Fallen, you will visit the Dimmed Bones ruins with Erend. As soon as you get to the top of the area with the ruins, you should see the scrap pile with the purple icon as soon as you arrive.
12) Thunderheads - During the main quest, Maker's End, you will have to go through two camps of Eclipse enemies, the second of which will have a Corruptor. After that, you will come upon a drop that will lead to a short scene revealing a Deathbringer. The path right before that drop houses the pile with the Ancient Vessel.