There isn't actually a great deal of customisation available in Doom: The Dark Ages... yet. You can only tweak the appearance of your weapons and the Slayer in minor ways, with each skin simply offering a new colour palette and nothing else. But how do you unlock these skins? That's actually quite simple. Let's talk about weapons first.
Each weapon offers four skin options. The first is the base Default design for the weapon that you get for first acquiring the weapon during a campaign playthrough. The other three are known as Revenant, Conqueror, and Nightmare.
Revenant & Nightmare: These are actually discovered throughout the story and found as dedicated secrets and collectibles in the many available levels. You'll have to do some exploring, but typically speaking, you should come across these quite easily.
Conqueror: This all-gold skin takes a bit more elbow grease as you first need to progress far enough through the campaign to unlock all of a weapon's upgrades, then spend the necessary resources to acquire them, before then also completing the Mastery Challenge that comes with spending a Wraithstone on the final upgrade.
If you need some help on this front, you can check out our guide that explores how to tick off all of the Mastery Challenges.
As for the Slayer, his skins are much more of a challenge to acquire as they're tied to the difficulty you beat the campaign on. Blast through the story on any difficulty and you'll get Nightmare, but if you want Revenant or Conqueror... Well, let's go into more depth.
For those unaware of what the latter two options mean, let me summarise.
Pandemonium: Same level of challenge as Nightmare, except when you die, Life Sigils (extra lives) can only be used to restart the chapter and not simply respawn and continue playing. Plus, if you run out of Life Sigils and then die, you lose that campaign save forever and have to start from scratch...
Ultra-Nightmare: Same level of challenge as Nightmare, but if you die, you lose that save file and have to start from scratch. Yep, this is the one death and it's game over difficulty for all the folk who truly like a brutal challenge.
Now it is worth saying that there are Atlan and Dragon skins too, and once we crack how to earn these - assuming you can through in-game activities - we'll be sure to update this guide.