How do I dye stuff in Minecraft PE?

Simple, get a cauldron and fill it with water. Then, grab the dye of your choice, and you can dye the water inside. Then, you can get your leather armor, right-click (Win10) the cauldron whilst holding the armor, and now it got dyed.

Thanks to this method, you can combine dyes in the cauldron, and still dye them with those colors.