You can procure dyes via the offhand gathering methods such as harvesting with a scythe as a botanist, spearfishing as fishermen, and quarrying as a miner. These offhand gathering points are visible via an icon on your map, whereas the mainhand gathering points can only be seen on screen by a visual sparkleyshine. you can also use this website.

Once you have obtained the dye of your choice, you must find/craft a suitable piece of gear that can be dyed by that color. Then you can apply the dye to the gear via the synthesis action, which requires that you be the appropriate class and lvl for the gear which you wish to dye.