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You can fill up vials by using various water sources such as water pumps, sinks and fountains. You can also use the Humidify spell in the Lunar spellbook which will fill all empty vials in your inventory. This requires a Magic level of 68, 1 Astral rune, 3 Water runes and 1 Fire rune.
Once you've filled a vial it turns into a Vial of water and it can be used to make potions.