Here's a video that shows off the new armor dyes added in the latest The Elder Scrolls Online update and the process of obtaining those dyes.
Dyes can be applied at various dying stations and are unlocked by achievements, so if you want to be the best dressed in Cyrodiil, get to work on those.
From the looks of the video dying is a a popular activity, at least until the novelty of the relatively frivolous feature wears off. The video creator, ChimneySwift11 can barely get to a dying station because of the rush