Weapon ascension materials are items that you need for ascending your weapons. Some of them can be obtained from enemy drops or exploring in the world, but the leftmost required item can only be obtained from the game's many domains, and two of them are for weapon ascension materials.
How to Farm Weapon Ascension Materials
The item drops from certain domains, like the ones for weapon ascension material, changes depending on what day it is.
You can view this by tapping on the item when you are able to ascend your weapon if it's at max level. It displays the days that it's available on, and tapping on it will show you where the domain's location is.
The other required ascension materials are often drops from certain enemies. Similar to the one above, you can view where they are from by tapping on the item.
If an item is from a boss, you will have to use your Adventure Handbook to view which enemy drops that item, then tap the "Navigate" button on the bottom right to find where they are.
Increasing your world level will increase the odds of the enemy dropping higher rarity items.
Weapon Ascension Items Usage
Boreal Wolf Items
Dandelion Gladiator Items
From Guyun Items
Mist Veiled Items
Enemy Drops Usage
Hilchurl Shooter Drops
Abyss Mage Drops
Fatui Cicin Mage Drops
Fatui Agent Drops
Fatui Skirmishers Drops
Treasure Hoarder Drops
Geovishap Hatchlings Drops
Domains to Farm Weapon Ascension Materials
Additionally, you can craft items from a lower tier to a higher tier by using the crafting bench, available in Mondstadt. This can help if you are getting unlucky with the drops, or if you just need a few more of it but out of resin to farm again.
Be sure to check if your characters have passive that can give you bonus during crafting or not before you start making some!