Dyes are used to dye wool, glass and leather armor.
To make red dye, you first need a red flower (Red flowers generate frequently in plains). After you have obtained the red flower, you place it anywhere on the 9 blocks of the crafting table or in the 4 plots of your inventory crafting box. 1 red flower makes 2 red dyes.
To make yellow dye, you first need a yellow flower (Yellow flowers generate frequently & randomly in plains). After you have obtained the yellow flower, you place it anywhere on the 9 blocks of the crafting table or in the 4 plots of your inventory crafting box. 1 yellow flower makes 2 yellow dyes.
To make orange dye, you have to have made a Yellow Dye and a Red Dye first. Then open up your crafting table inventory. After that, you put the red and yellow dyes anywhere on the crafting grid. This makes 2 orange dyes.
While it is available in the creative inventory, it cannot be used to dye items. Lapis lazuli is used for dying items blue. The blue dye item can be used for crafting the party hat, however.
To make green dye, first you must obtain a block of cactus. Then you must smelt the cactus in a furnace. This makes 1-2 green dyes.
Cyan dye (a.k.a teal dye) is made by putting a blue dye and a green dye in a crafting grid. This makes 2 cyan dyes.
Although a brown dye item does not exist, cocoa beans can be used to dye wool and glass brown. Unlike other dyes, cocoa beans cannot dye leather armor or be used to craft party hats.
Bone meal can be used to lighten dyes or cloths. To do this put bone meal anywhere on the crafting grid with the dye/cloth. The only dyes that can be lightened are red (to make pink) and lapis lizuli (to make light blue), however, black wool can be lightened to make grey wool (which can be further lightened to make light grey wool). 1 dye and 1 bone meal makes 2 light dyes. Bone meal can also be used to make party hats.
Yellow flower (craft) - 2 yellow dye
Red flower (craft) - 2 red dye
Cactus (smelt) - 1 green dye
Red and yellow dye (craft) - 2 orange dye
Lapis lazuli and bone meal (craft) - 2 light blue dye
Lapis lazuli and red dye (craft) - 2 purple dye
Green dye and bone meal (craft) - 2 lime dye
Red dye and bone meal (craft) - 2 pink dye
Green dye and lapis lazuli (craft) - 2 cyan dye
Pink and purple dye (craft) - 2 magenta dye