How to make banner designs in Minecraft: loom and patterns
Put a banner and a dye in a Loom, pick a pattern and take the result:

Dye is the colorant of Minecraft, in 16 colors, used to tint blocks, items and even animals.
It is made with the Crafting Table from Bone Meal (other recipes also exist).
Most dyes come from flowers, crafted one by one; others come from Ink Sac, Cocoa Beans, Lapis Lazuli, Bone Meal, cactus, beetroot or sea pickles, and two dyes can be mixed into a third color. Wandering traders also sell them.
Use a dye on a sheep, a wolf's or cat's collar, or a sign to color its text. In the crafting grid it tints wool, glass, terracotta, concrete powder, candles, beds, shulker boxes, bundles and leather armor, and at a loom it draws banner patterns.
Bone Meal → White Dye
// Slots with several items cycle through every accepted option.
Put a banner and a dye in a Loom, pick a pattern and take the result:
There are 16 colors, and you can recolor any harness by crafting it with a dye.
Smelt Clay into Terracotta; 8 Terracotta and 1 Light Gray Dye give 8 Light Gray Terracotta.
At the Crafting Table: 1 × Bone Meal gives 1 × Dye. It can be found as loot in Village and Trail Ruins. Sold by Wandering Trader. Bought by Villager: Shepherd (Apprentice).
It colors blocks, items, sheep, collars and sign text. It is an ingredient in 21 recipes, made at the Crafting Table; for example White Harness, White Wool, White Wool Slab, White Wool Stairs, White Bundle and 13 more.